Highlighted Articles Published by İTÜ's Mathematics Engineering Department in 2025
The ITU Department of Mathematics Engineering has had a remarkable first half of 2025, marked by significant academic achievements and groundbreaking research. Faculty members and students have been recognized for their contributions to advancing mathematical knowledge, publishing in prestigious journals, and participating in impactful interdisciplinary projects. These accomplishments highlight the department’s dedication to excellence in both research and education. By fostering a collaborative and innovative academic environment, ITU Mathematics Engineering continues to expand the boundaries of theoretical and applied mathematics. As the year progresses, the department looks forward to building on this momentum, driving forward innovation, and addressing complex challenges across diverse fields.
Hopf bifurcation in the shadow of extinction: Collaborating with epidemic dynamics through lethal mutations and declining ancestor infections
The article entitled “Hopf bifurcation in a generalized Goodwin model with delayHopf bifurcation in the shadow of extinction: Collaborating with epidemic dynamics through lethal mutations and declining ancestor infections”, authored by ITU Department of Mathematics members Assoc. Prof. Dr. Ali Demirci, Assoc. Prof. Dr. Ayşe Peker-Dobie, Assoc. Prof. Dr. Cihangir Özemir and Prof. Dr. Semra Ahmetolan was published in BioSystems.
This study presents a mathematical framework that couples epidemic dynamics with adaptive human behavior through a system of nonlinear differential equations. Unlike traditional SIR models with fixed parameters, the authors introduce a dynamic feedback mechanism in which individual social activity evolves endogenously based on utility maximization. At the heart of the model is a utility function that weighs the benefits of social engagement against the risk of infection. The resulting behavioral response influences the contact rate in the epidemic model, creating a coupled system where disease progression and human behavior co-determine each other over time. The paper’s main mathematical contribution lies in the rigorous formulation and analysis of this interaction. The authors investigate the system's equilibria and stability properties, providing conditions for the existence and uniqueness of solutions. Their analysis demonstrates how behavioral adaptation alters the system’s trajectory, enabling the emergence of dynamic suppression effects or prolonged endemic states. By embedding individual-level optimization directly into the epidemic process, the model offers a tractable structure for studying feedback-rich public health systems. This approach represents a valuable extension of classical dynamical systems in epidemiology, integrating behavioral economics into a formal continuous-time framework.
https://doi.org/10.1016/j.biosystems.2025.105406.
Hopf bifurcation in a generalized Goodwin model with delay
The article entitled “Hopf bifurcation in a generalized Goodwin model with delay”, authored by ITU Department of Mathematics members Postdoctoral Researcher Dr. Ayşe Tiryakioğlu, Assoc. Prof. Dr. Ayşe Peker-Dobie and Assoc. Prof. Dr. Cihangir Özemir, with graduate student Eyşan Şans and undergraduate student Melisa Akdemir was published in Mathematics and Computers in Simulation.
Goodwin’s model is a cornerstone in the study of dynamical systems within macroeconomics, explaining the interaction between employment ratio and wage share in a closed economy. Analogous to predator-prey dynamics in mathematical economics, the Goodwin model, despite its simplicity, effectively captures the periodic behavior of state variables over specific time intervals. By relaxing the initial assumptions, the model can be adapted to account for more complex economic scenarios. In this article, we study a higher-dimensional extension of the Goodwin model that incorporates variable capacity utilization and capital coefficient alongside employment ratio and wage share. In particular instances, the wage share and employment rate equations decouple from the overall system. For these cases, by incorporating a delay effect in the Phillips curve, we demonstrate that while the equilibrium of the generalized system remains stable within certain parameter domains in the absence of delay, the introduction of delay can induce a Hopf bifurcation, leading to periodic oscillations. We analytically derive the critical delay parameter value that destabilizes the equilibrium point via a Hopf bifurcation.
This work is based on results of a summer academic internship with the undergraduate student Melisa Akdemir and the Master’s thesis of the graduate student Eyşan Şans, both conducted by C. Özemir.
https://doi.org/10.1016/j.matcom.2025.04.012.
Covariant Differential Calculi on a New Z3-graded Quantum Group and Space
The article titled “A New Z₃-Graded Quantum Space and Its Geometry” authored by ITU Department of Mathematics Engineering faculty member Assoc. Prof. Dr. Ayşe Peker Dobie, Assoc. Prof. Dr. Sultan A. Çelik (Department of Mathematics, Yıldız Technical University), Assoc. Prof. Dr. Fatma Bulut (Department of Mathematics, Bitlis Eren University), and Dr. İlknur Temli (Yıldız Technical University), was published in International Journal of Theoretical Physics.
This study introduces a novel Z₃-graded quantum group GLq(1|1|1), constructed from 3×3 matrices via an R-matrix formalism, along with its associated graded quantum space Cq¹|¹|¹. The group is endowed with a Hopf algebra structure and serves as a symmetry object for the underlying graded geometry.
Two distinct Z₃-graded differential calculi are developed on the corresponding function and exterior algebras. Explicit commutation relations for the first- and second-order differentials are derived, ensuring covariance under the Hopf algebra action and compatibility with Z₃-grading.
This framework extends earlier results in graded quantum geometry and provides new tools for the study of noncommutative differential structures with potential applications in mathematical physics.
https://doi.org/10.1007/s10773-025-05947-1 .
Manipulating the Hopf and Generalized Hopf Bifurcations in an Epidemic Model via Braga’s Methodology
The article titled “Manipulating the Hopf and Generalized Hopf Bifurcations in an Epidemic Model via Braga’s Methodology,” authored by ITU Department of Mathematics Engineering faculty member Assoc. Prof. Dr. Ayşe Peker-Dobie, was published in International Journal of Bifurcation and Chaos.
This study investigates bifurcation control in a Susceptible-Infectious epidemic model with two clinical forms of infection—non-lethal and lethal—arising from the same pathogen. Using Braga’s control methodology, a four-parameter feedback law is applied to regulate Hopf and generalized Hopf bifurcations at an equilibrium representing dominance of a mutated, more lethal viral strain.
Conditions for codimension-1 and codimension-2 bifurcations are established, and the influence of control parameters on the stability and amplitude of periodic solutions is demonstrated. Simulations illustrate transitions from foci to limit cycles, including coexistence of stable and unstable oscillations.
Unlike classical compartmental models, this approach incorporates interventions directly into the system’s dynamics. This maintains structural simplicity while enabling precise bifurcation control. The framework offers valuable insights for designing intervention strategies in epidemics shaped by viral mutation and nonlinear oscillatory behavior.
https://doi.org/10.1142/S0218127425500932.
Control of Hopf and Bautin bifurcation in a modified Goodwin model of growth cycle
The article titled “Control of Hopf and Bautin bifurcation in a modified Goodwin model of growth cycle” authored by by ITU Department of Mathematics Engineering faculty members Assoc. Prof. Dr. Ayşe Peker Dobie, Assoc. Prof. Dr. Cihangir Özemir, and Melike Nur Erdoğan, was published in International Journal of Dynamics and Control.
This study examines Hopf and Bautin bifurcations in a modified Goodwin model of growth cycles. Using a control method based on normal form theory, a feedback law is introduced that regulates periodic dynamics. The results show how parameter tuning can stabilize or eliminate economic fluctuations, providing insights for designing effective macroeconomic policy interventions.
The Goodwin model captures macroeconomic cycles through a predator–prey framework linking wage share and employment. A modified version introduced by Desai et al. (2006) is analyzed, incorporating a nonlinear Phillips curve and constraints to ensure economically realistic trajectories.
Using a feedback control approach based on normal form theory, the study explores how a two-parameter control input governs Hopf and Bautin bifurcations. Hopf control adjusts the first Lyapunov coefficient to induce or suppress oscillations. Bautin bifurcation arises when the first Lyapunov coefficient vanishes and the second is nonzero, yielding coexisting stable and unstable cycles.
Simulations confirm transitions from foci to nested limit cycles. This control-based framework offers practical tools for regulating macroeconomic fluctuations.
This work is based on results of the Master’s thesis of the graduate student Melike Nur Erdoğan conducted by A. Peker Dobie.
https://doi.org/10.1007/s40435-025-01663-0 .
Analytical and algebraic insights to the generalized Rosenau equation: Lie symmetries and exact solutions
The article entitled “Analytical and algebraic insights to the generalized Rosenau equation: Lie symmetries and exact solutions”, authored by ITU Department of Mathematics Engineering faculty member Assoc. Prof. Dr. Cihangir Özemir, Postdoctoral Researcher Dr. Ayşe Tiryakioğlu, and Özemir’s PhD student Yasin Hasanoğlu, was published Chaos, Solitons & Fractals. This work was supported by Scientific Research Projects Department of Istanbul Technical University, Project Number: TGA-2024-45496.
This work presents a comprehensive group-theoretical investigation of a generalized Rosenau equation with arbitrary nonlinear terms. The primary objective is to explore the symmetry structure of the equation using Lie group analysis and to classify specific families of Rosenau-type equations that admit Lie symmetries. The analysis begins by determining the Lie point symmetries of the equation and identifying the corresponding Lie algebras for several distinct nonlinear forms.
Utilizing the optimal system of one-dimensional subalgebras, the resulting partial differential equations (PDEs) are systematically reduced to ordinary differential equations (ODEs). These reductions significantly simplify the original problem and allow for the derivation of exact analytical solutions for select cases. In particular, the focus is placed on equations with cubic, quintic, and cubic–quintic nonlinearities, for which explicit traveling wave solutions of both hyperbolic and elliptic type are constructed. In addition, new kink-type soliton solutions and sech-type soliton solutions are obtained, enriching the variety of exact solutions for the system.
The analysis is further extended by considering physically motivated nonlinearities, such as power-law and exponential forms. These types are derived based on realistic assumptions in modeling physical systems and are shown to be compatible with the symmetry classifications obtained earlier.
The results confirm that the generalized Rosenau equation exhibits rich mathematical structure and integrability properties, making it a useful model in the study of nonlinear wave phenomena.
To access the full article, https://doi.org/10.1016/j.chaos.2025.116263 .
On space-like class A surfaces in Robertson–Walker spacetimes
The research titled "On space-like class A surfaces in Robertson–Walker spacetimes" by Prof. Dr. Nurettin Cenk Turgay, faculty member of the Department of Mathematics Engineering, has been published in Mathematische Nachrichten. The study was coauthored by Assoc. Prof. Dr. Burcu Bektaş Demirci (Fatih Sultan Mehmet Vakif University) and Assoc. Prof. Dr. Rüya Yeğin Şen (İstanbul Medeniyet University).
In this work, they investigate space-like in the Robertson-Walker spacetime . They first characterize surfaces for which the tangent component of the co-moving observer field is an eigenvector of all shape operators. These are termed class A surfaces. Subsequently, they establish a local classification theorem for class A surfaces in . As an application of this result, they derive local parameterizations for space-like surfaces where the normal component of the unit vector field when the normal part of the unit vector field is parallel.
To access the full article, https://doi.org/10.1002/mana.202400374 .
Biconservative Surfaces in Robertson–Walker Spaces
The research article titled "Biconservative Surfaces in Robertson–Walker Spaces" by Prof. Dr. Nurettin Cenk Turgay faculty member of the Department of Mathematics, has been published in Results in Mathematics. The study was coauthored by Assoc. Prof. Dr. Rüya Yeğin Şen (İstanbul Medeniyet University).
This study contributes to the theory of differential geometry by exploring biconservative isometric immersions with parallel mean curvature vector (PMCV) in Robertson–Walker spacetimes, which are important models in cosmology. The authors first investigate geometric properties of biconservative surfaces in the Lorentzian warped product spaces , and then provide complete local classifications for PMCV surfaces in the cases , , and . Finally, they globally proved that a space-like PMCV biconservative surface in , for lies within a totally geodesic submanifold of dimension or .
To access the full article, https://doi.org/10.1007/s00025-025-02395-5 .
The effects of Co/Ce co-doped ZnO thin films: an optical and defect study
The article titled “The effects of Co/Ce co-doped ZnO thin films: an optical and defect study”, co-authored by ITU Department of Mathematics faculty member Prof. Dr. Ersin Özuğurlu and member of the Bahçeşehir University Prof. Dr. Lütfi Arda, was published in Journal of Materials Science: Materials in Electronics. In this study, the authors explore how co-doping with cobalt and cerium influences the structural and optical properties of ZnO thin films, offering valuable data for next-generation optoelectronic applications.
Ce-doped ZnCoO (Zn0.99-xCo0.01CexO) thin flms (with x = 0.00 to 0.05 in increments of 0.01) were grown using the sol–gel technique to investigate the influence of defects on their optical properties. By applying a Double Facet Coated Substrate (DFCS) theoretical transmitance model to analyze the optical transmitance data, the thickness, absorption loss, extinction coefcient, and refractive index of the thin flms were determined.
This study contributed to the following fields in industry:
• Advances optical modeling (DFCS method) for thin-film characterization.
• Enhances defect engineering in ZnO for optoelectronic applications.
• Provides key optical parameters for semiconductor device design.
• Offers a scalable synthesis approach (sol-gel) for industrial adoption.
The insights from this study could lead to better-performing transparent electronics, improved photolithographic processes, and optimized optoelectronic devices, making it highly relevant for both academic research and industrial R&D.
To access the full article, https://doi.org/10.1007/s10854-025-14890-0 .
Removing Salt-and-Pepper Noise with the Power of Fractional Calculus
The article titled “Full fractional total variation method for eliminating salt and pepper noise,” authored by Dr. Evren Tanrıöver (Teaching Assistant), Prof. Dr. Ahmet Kırış, and Prof. Dr. Burcu Tunga (Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University), and Prof. Dr. M. Alper Tunga (Department of Computer Engineering, Faculty of Engineering and Natural Sciences, Istinye University), was published in Signal, Image and Video Processing (2025).
This study presents a new hybrid filter, TVFFS&P, designed to effectively remove salt-and-pepper noise. It combines the Full Fractional Total Variation (TVFF) method—originally effective against Gaussian noise—with two linear filters. By using fractional derivatives and nonlocal parameters, the method enhances denoising performance. Experiments show that TVFFS&P outperforms existing methods, especially under high noise, while preserving image details.
A recent study introduces a novel hybrid filter, named TVFFS&P, developed to effectively eliminate salt-and-pepper noise from grayscale images. This innovative filter combines the strengths of two linear filters with the Full Fractional Total Variation (TVFF) method, a technique based on fractional calculus that has proven successful in removing Gaussian noise. The TVFF method utilizes Riesz–Caputo and Caputo fractional derivatives in both spatial and temporal domains, along with nonlocal length-scale parameters, allowing more accurate modeling of pixel interactions.
Unlike traditional median filters or adaptive filters that may blur fine details, the TVFFS&P filter strategically integrates linear and nonlinear techniques to preserve edge information while cleaning noisy pixels. The hybrid algorithm is applied in three stages, ensuring that even heavily corrupted images are restored effectively.
Performance evaluations across standard benchmark and medical images show that TVFFS&P significantly outperforms other state-of-the-art methods, especially under high noise intensities (up to 90%). Evaluation metrics such as PSNR, SSIM, and MS-SSIM confirm its superiority in both noise reduction and detail preservation.
This method represents a promising direction for applications in medical imaging, remote sensing, and other areas where image clarity is essential. The authors also provide an open-source implementation on GitHub for further development and testing.
To access the full article, https://doi.org/10.1007/s11760-025-04047-1 .
Generalized Taylor Series and Peano Kernel Theorem
The article titled “Generalized Taylor Series and Peano Kernel Theorem”, authored by ITU Department of Mathematics Engineering faculty member Dr. Fatma Zürnacı Yetiş and Prof. Dr. Çetin Dişibüyük (Dokuz Eylül University), was published in Mathematical Methods in the Applied Sciences.
This study introduces a novel generalization of the classical Taylor series using non-polynomial divided differences, offering a unified approach to interpolation, approximation, and integration across various functional spaces.
As in the polynomial case, non-polynomial divided differences can be viewed as a discrete analog of derivatives. This link between non-polynomial divided differences and derivatives is defined by a generalization of the derivative operator. In this study, a generalization of the Taylor series is obtained using the connection between non-polynomial divided differences and derivatives, and a generalized Taylor theorem is stated. With the definition of a definite integral, the relation between the non-polynomial divided difference and non-polynomial B-spline functions is expressed in terms of integration. A general form of the Peano kernel theorem is also derived, based on a generalized Taylor expansion with an integral remainder. As in the polynomial case, it is shown that non-polynomial B-splines are in fact the Peano kernels of non-polynomial divided differences.
Taylor series are important for the problem of representing an arbitrary function by means of linear combinations of prescribed functions. The ordinary Taylor series has been generalized by many authors. In this study, a generalization of the Taylor series is obtained for a broad class of function spaces, including standard polynomials, trigonometric polynomials, hyperbolic polynomials, and special Müntz spaces. A significant distinction between the generalized and classical Taylor series is that while the classical Taylor series approximates a function using polynomials, the generalized version uses functions from a more extensive range of function families. Numerical examples demonstrate that the generalized approach yields improved approximations compared to the classical Taylor series. These new approximations have potential applications in any context where classical Taylor series are traditionally used. Additionally, a new generalization of the Peano kernel theorem is developed, providing a powerful tool for estimating errors in approximation methods such as interpolation, quadrature rules, and B-splines. This generalization is constructed based on the generalized Taylor expansion. A connection is established between non-polynomial B-splines and the Peano kernels of non-polynomial divided differences, and it is demonstrated that, as in the polynomial case, non-polynomial B-splines function as Peano kernels of the associated divided differences.
To access the full article, https://doi.org/10.1002/mma.10616 .
Long time behavior of solutions to the generalized Boussinesq equation
The article entitled “Long time behavior of solutions to the generalized Boussinesq equation” conducted by ITU Department of Mathematics member Prof. Dr. Gülçin M. Muslu, in collaboration with Assoc. Prof. Dr. Amin Esfahani (Nazarbayev University) has been published in Analysis and Mathematical Physics.
In this paper, the generalized Boussinesq equation (gBq), considered as a model for water wave dynamics with surface tension, is investigated. The study begins with an analysis of the initial value problem in Sobolev spaces, deriving improved conditions for global existence and finite-time blow-up of solutions—extending earlier results to lower Sobolev indices. The time-decay behavior of solutions is further explored in Bessel potential and modulation spaces, where global well-posedness and time-decay estimates are established. Using Pohozaev-type identities, the non-existence of solitary waves is demonstrated for specific parameter regimes.
A significant contribution of this work is the numerical generation of solitary wave solutions for the gBq equation using the Petviashvili iteration method. In addition, a Fourier pseudo-spectral numerical method is proposed to study the time evolution of solutions, particularly addressing the gap interval where theoretical results regarding global existence or blow-up remain unavailable in Sobolev spaces. The numerical results confirm theoretical predictions in applicable cases and provide novel insights in previously unexplored parameter regimes. This comprehensive analysis clarifies the theoretical and numerical landscape of the gBq equation and introduces valuable tools for future research.
To access the full article, https://doi.org/10.1007/s13324-025-01048-8 .
Innovative deep learning approach for cross-crop plant disease detection: A generalized method for identifying unhealthy leaves
A new study titled “Innovative deep learning approach for cross-crop plant disease detection: A generalized method for identifying unhealthy leaves” was recently published in Information Processing in Agriculture. The article is co-authored by Prof. Dr. Muhammed Kurulay from the Department of Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University, alongside researchers from LabSTIC Laboratory at Guelma University in Algeria.
The study tackles one of the most persistent challenges in agricultural AI: building a reliable model that can detect diseases across different crop types and disease categories, including those not represented in training data. Traditional deep learning models often lack generalization capabilities, performing well only within narrow, dataset-specific contexts. To address this, the authors propose a deep learning-based classification framework that detects disease symptoms at the patch level rather than relying on whole-leaf features. This method decouples disease recognition from crop-specific characteristics.
By segmenting each leaf image into 32×32 pixel patches and focusing on identifying unhealthy regions, the system achieves a high degree of generalization. The model is based on a compact Inception architecture, optimized to handle small inputs efficiently. The team trained and tested the model using a customized version of the widely recognized PlantVillage dataset and validated it with real-world samples from the PDDB dataset, achieving accuracy rates of 94.04% and 97.22% respectively.
Notably, the model can assess the extent of infection by estimating the prevalence of unhealthy patches, offering not only detection but also quantification. This is a crucial advancement for scalable, real-time disease monitoring in agriculture.
By overcoming the limitations of crop- and disease-specific training, this research presents a robust and scalable tool for early plant disease detection—supporting global food security efforts and modernizing disease management in precision agriculture.
To access the full article, https://doi.org/10.1016/j.inpa.2024.03.002.
Comparison of cobalt phthalocyanine (CoPc) and reduced graphene oxide functionalized CoPc hybrid as sensing element for heavy metal ions in water
The article titled “Comparison of cobalt phthalocyanine (CoPc) and reduced graphene oxide functionalized CoPc hybrid as sensing element for heavy metal ions in water”, authored by ITU Department of Mathematics Engineering faculty member Prof. Dr. Murat Sarı, Prof. Dr. Erol Kam (Energy Institute, Istanbul Technical University) and Prof. Dr. Ahmet Altındal (Faculty of Science and Letters, Department of Physics Engineering, Istanbul Technical University) was published in Synthetic Metals.
This study evaluates quartz crystal microbalance sensors coated with cobalt phthalocyanine (CoPc) and a reduced graphene oxide–CoPc hybrid for detecting arsenic, mercury, lead, and cadmium ions in water. The rGO/CoPc composite exhibited significantly higher sensitivity and stability, achieving 3.9 × 10⁴ Hz·L·mg⁻¹ for As³⁺ and retaining 95 % sensitivity after 500 h, outperforming pristine CoPc.
In response to escalating concerns over toxic heavy metal contamination in surface waters, researchers compared two sensing coatings—pristine cobalt phthalocyanine (CoPc) and a reduced graphene oxide–CoPc (rGO/CoPc) hybrid—using quartz crystal microbalance (QCM) technology. Both coatings were deposited on QCM electrodes and exposed to aqueous solutions containing arsenic (As³⁺), mercury (Hg²⁺), lead (Pb²⁺), and cadmium (Cd²⁺) ions.
Adsorption equilibrium isotherms were measured and fitted to five common models (Langmuir, Freundlich, Elovich, Temkin, and Jovanovic). The rGO/CoPc sensor’s carboxyl-rich, Lewis-basic surface dramatically improved adsorption affinity and sensitivity for all four ions. Notably, As³⁺ detection sensitivity rose from 6.7 × 10² Hz·L·mg⁻¹ with CoPc to 3.9 × 10⁴ Hz·L·mg⁻¹ with rGO/CoPc.
Long-term stability tests for Pb²⁺ sensing over ~500 hours showed the rGO/CoPc hybrid maintained about 95 % of its initial response, compared to only 80 % retention by the CoPc sensor. Regression analyses confirmed stronger adsorption constants and higher correlation coefficients for the composite, indicating more reliable quantification at trace levels.
By combining the extended π-conjugation and tunable chemistry of metallophthalocyanine with the oxygen-functionalized network of rGO, the study demonstrates a robust, in situ QCM sensing platform for environmental monitoring. These findings pave the way for portable, cost-effective devices capable of real-time heavy metal surveillance in water supplies.
To access the full article, https://doi.org/10.1016/j.synthmet.2025.117877 .
Initial data identification in advection–diffusion processes via a reversed fixed-point iteration method
The article titled “Initial data identification in advection–diffusion processes via a reversed fixed-point iteration method” co-authored by ITU Department of Mathematics Engineering faculty member Prof. Dr. Murat Sarı and Assist. Prof. Dr. Tahir Coşgun (Department of Mathematics, Faculty of Science and Letters, Yıldız Technical University; and Department of Mathematics, Amasya University), was published in Mathematical Methods in the Applied Sciences .
This work introduces the reversed fixed-point iteration method (RFPIM) for recovering initial concentration profiles in linear advection–diffusion systems from noisy final-time measurements. Numerical experiments with noise levels up to 100 % demonstrate robust reconstruction capabilities. The approach, previously used for unstable equilibria in Banach spaces, proves effective as an inverse solver for advection–diffusion equations under varying signal-to-noise conditions.
Accurate determination of initial conditions in advection–diffusion phenomena is crucial for modeling contaminant transport, pollutant dispersion, and heat transfer in environmental and engineering contexts. Traditional forward solvers cannot invert noisy final-time data to retrieve the original state, especially under high Péclet numbers where advection dominates. To address this inverse problem, the present study adapts the reversed fixed-point iteration method (RFPIM)—originally developed for locating unstable equilibria of nonlinear mappings in Banach spaces—to the linear advection–diffusion equation.
The algorithm iteratively back-propagates the observed final profile, using a hybrid scheme that couples RFPIM with standard finite-difference discretization. At each iteration, the method applies an integral operator criterion to ensure convergence toward a repelling fixed point corresponding to the true initial data. Stability analysis confirms the scheme’s resilience to discretization and rounding errors, while numerical tests assess performance under synthetic measurement noise levels of 5 %, 10 %, 30 %, 50 %, and 100 %.
Results reveal that RFPIM successfully reconstructs smooth and sharply varying initial profiles even when the final data is highly corrupted. Error norms remain below 10 % for noise up to 50 %, and key features of the initial state are preserved at 100 % noise. These findings underscore RFPIM’s potential as a powerful tool for inverse modeling in environmental monitoring, subsurface hydrology, and any application requiring reliable recovery of pre-event concentration fields. Future work will extend this framework to fractional and nonlinear advection–diffusion models.
To access the full article, https://doi.org/10.1002/mma.8999 .
Traveling waves reflecting various processes represented by reaction–diffusion equations
The article titled “Traveling waves reflecting various processes represented by reaction–diffusion equations,” authored by ITU Department of Mathematics Engineering faculty member Prof. Dr. Murat Sarı, Assoc. Prof. Dr. Asıf Yokuş (Fırat University), Assoc. Prof. Dr. Serbay Duran (Adıyaman University), and Assoc. Prof. Dr. Hülya Durur (Ardahan University), was published in Mathematical Methods in the Applied Sciences.
This paper derives new traveling wave solutions for a two-species reaction–diffusion system with external forcing, using an expansion (G′/G) method. Exact hyperbolic, trigonometric, and rational waveforms are obtained and analyzed for varying diffusion coefficients and source terms. The study reveals how parameter choices produce soliton-like behavior, Turing-pattern diffusion, and extinction vortices, offering insights into spatiotemporal population dynamics.
Reaction–diffusion equations model many spatiotemporal phenomena—from chemical concentrations to biological populations—by combining local reactions with spatial diffusion. When external forcing terms and non-monotonic interactions are present, classical analytical methods often fail to capture complex behaviors. This work applies the G^'/G expansion method to a two-species system with diffusion coefficients d_1,d_2, nonlinear interaction terms G_1 (u,v),G_2 (u,v), and source functionsf_1 (x,t),f_2 (x,t).
By introducing a traveling wave ansatz, the authors reduce the partial differential system to ordinary differential equations in a moving coordinate frame. The G^'/G technique then generates three families of exact solutions—hyperbolic (soliton), trigonometric (periodic), and rational forms—each parameterized by arbitrary constants tied to wave speed and forcing strength. Illustrative plots demonstrate how increasing d_2 broadens wave fronts, while variation in external forcing induces hexagonal Turing-pattern diffusion at different times.
Physical interpretation shows that soliton solutions correspond to invasion waves of a species into a new habitat, with amplitude and velocity controlled by reaction rates and diffusion contrasts. When parameters satisfy specific dispersion relations, the wave breaks into an extinction vortex, indicating population collapse. These analytical solutions elucidate the relationship between model parameters and emergent patterns, guiding experimental and numerical studies in ecology, epidemiology, and material science. Future work will extend this framework to higher-dimensional and fractional reaction–diffusion systems.
To access the full article, https://doi.org/10.1002/mma.10493 .
Deep learning aided surrogate modeling of the epidemiological models
The article titled “Deep learning aided surrogate modeling of the epidemiological models,” authored by ITU Department of Mathematics Engineering faculty member Prof. Dr. Murat Sarı, PhD student Emel Kurul and Prof. Dr. Nuran Güzel (Department of Mathematics, Faculty of Science and Letters, Yıldız Technical University), Assist. Prof. Dr. Hüseyin Tunç (Department of Biostatistics and Medical Informatics, School of Medicine, Bahçeşehir University), and was published in Journal of Computational Science.
The study introduces a deep neural network surrogate modeling (DNN-SM) framework that emulates compartmental epidemiological models—such as SIR, SEIR, and SEPADR—with high fidelity, while significantly reducing computational costs. Trained on solution trajectories generated by conventional ODE solvers, the DNN-SM model predicts disease dynamics and performs parameter estimation approximately ten times faster than traditional methods. The framework is validated using COVID-19 data from several European countries.
Compartmental models like SIR, SEIR, and SEPADR are essential for analyzing infectious disease spread, yet they present substantial computational demands when applied to real-time inference or extensive parameter sweeps. To address these challenges, the proposed DNN-SM pipeline generates large-scale training datasets by solving the underlying models over a wide range of parameters using standard numerical solvers. These time-series outputs—representing key epidemiological compartments—serve as training data for feed-forward neural networks.
Through hyperparameter tuning in MATLAB and Python, architectures are selected to optimize both accuracy and efficiency. Once trained, the DNN-SM is capable of producing fast and reliable forward simulations without the need for repeated ODE integration. For parameter estimation tasks, the surrogate model is embedded in an optimization routine, allowing for rapid model fitting by minimizing the discrepancy between real data and surrogate output.
The framework is applied to real-world COVID-19 case data from multiple European nations, demonstrating its ability to reproduce outbreak dynamics, latent trends, and endemic behaviors with high accuracy. By offering a substantial speed-up in simulation and inference, the DNN-SM method supports rapid scenario analysis and timely decision-making in public health settings, particularly during evolving epidemic situations.
To access the full article, https://doi.org/10.1016/j.jocs.2024.102470 .
A modified Davey–Stewartson system of nonlinear dust acoustic waves in (3+1) dimensions: Lie symmetries and exact solutions
The article titled “A modified Davey–Stewartson system of nonlinear dust acoustic waves in (3+1) dimensions: Lie symmetries and exact solutions,” authored by Research Assistant Şeyma Gönül, PhD students Yasin Hasanoğlu and Yasemin Çalış, Postdoctoral Researcher Dr. Ayşe Tiryakioğlu, and Assoc. Prof. Dr. Cihangir Özemir from the Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, was published in European Physical Journal Plus.
The study analyzes a modified Davey–Stewartson (DS) system arising in the context of nonlinear dust acoustic wave propagation in three-dimensional plasma media. Distinguished by an additional term interpreted as a constant complex potential, this system differs from classical DS-type equations. The authors primarily investigate whether this extra term can be eliminated through a transformation of the dependent and independent variables. It is shown that, under a specific condition on the system’s parameters, the term can indeed be removed, leading to a simplified version of the system.
Subsequently, the Lie symmetry algebra of the modified DS system is examined in both cases—when the term is removable and when it is not. The resulting algebra is identified as a semi-direct sum of a finite-dimensional Lie algebra with a Kac–Moody algebra, illuminating the group-theoretical structure of the system and revealing links to known results. These findings open avenues for systematic reductions to lower-dimensional equations, in line with approaches used in related studies.
The authors also construct exact solutions for several scenarios, focusing on generalized traveling wave forms. These include line soliton and kink soliton–line soliton solutions, which capture the dynamic interplay between short-wave and long-wave components propagating perpendicular to each other within plasma environments.
This work provides a new perspective on the modified DS system, which has not previously been studied in this way. By combining symmetry analysis, exact solutions, and connections to physically motivated plasma models, the study highlights the system’s rich mathematical structure and physical relevance. The results are expected to encourage further research on similar nonlinear wave models in plasma physics.
To access the full article, https://doi.org/10.1140/epjp/s13360-025-06429-3 .