Publications

• Title: Algorithm-assisted individualized therapy design improves survival in a mouse model of triple-negative breast cancer
• Authors: Balázs Gombos; Violetta Léner; Dániel András Drexler; Bence Czakó; Tamás Ferenci; Levente Kovács; Dániel Kiss; Pál Szabó; József Tóvári; Gergely Szakács; András Füredi
• Abstract: Chemotherapy remains indispensable in the treatment of malignant tumors but is often limited by the prevailing “one size fits all” approach, which neglects inter-patient variablity in pharmacokinetics and treatment response, often resulting in suboptimal outcomes. In this study, we explored individualized chemotherapy protocols in a clinically relevant mouse model of breast cancer using a novel algorithm-assisted therapy design (AATD). Two strategies were applied: a two-stage computational therapy protocol designed to stabilize blood concentrations of pegylated liposomal doxorubicin (PLD); and a model-predictive approach that optimizes dosing based on individual tumor characteristics. Compared to the standard maximum tolerated dose protocol, AATD-based personalized chemotherapy, guided by real-time monitoring of treatment response, tumor growth, and drug concentrations, significantly improved overall survival. Our findings in a mouse model of triple-negative breast cancer provide compelling evidence that chemotherapy can be personalized and optimized through algorithm-assisted therapy design.
• Journal/Conference: npj Precision Oncology
• Publication Date: 2026 (Article in Press; received 25 Oct 2025, accepted 9 Dec 2025)
• Volume: Article in Press (final volume/issue TBD)
• Article/Pages: Article in Press (pages TBD)
• Keywords: Cancer; Personalized medicine; Pegylated liposomal doxorubicin (PLD); Genetically engineered mouse model; Algorithm-assisted therapy design; Maximum tolerated dose; Model predictive control; Pharmacokinetics/pharmacodynamics
• Contact (corresponding author): Dániel András Drexler, drexler.daniel@nik.uni-obuda.hu (also: András Füredi, furedi.andras@ttk.hu; Gergely Szakács, szakacs.gergely@ttk.hu)
• Doi: 10.1038/s41698-025-01245-5

• Title: First Integrals and Invariants of Systems of Ordinary Differential Equations
• Authors: Mateja Grašič; Abdul Salam Jarrah; Valery G. Romanovski (corresponding author)
• Abstract: We investigate the interplay between monomial first integrals, polynomial invariants of certain group action, and the Poincaré–Dulac normal forms for autonomous systems of ordinary differential equations with a diagonal matrix of the linear part. Using tools from computational algebra, we develop an algorithmic approach for identifying generators of the algebras of monomial and polynomial first integrals, which works in the general case where the matrix of the linear part includes algebraic complex eigenvalues. Our method also provides a practical tool for exploring the algebraic structure of polynomial invariants and their relation to the Poincaré-Dulac normal forms of the underlying vector fields.
• Journal/Conference: Mathematics (MDPI)
• Publication Date: 1 November 2025
• Volume: 13
• Issue: 21
• Article number: 3485
• Keywords: first integrals; polynomial invariants; Poincaré-Dulac normal form; systems of ordinary differential equations
• Contact: Valery G. Romanovski (valerij.romanovskij@um.si)
• DOI: 10.3390/math13213485

• Title: Fractal zeta functions at infinity and the ϕ\phiϕ-shell Minkowski content
• Authors: Goran Radunović (University of Zagreb)
• Abstract: We study fractal properties of unbounded domains with infinite Lebesgue measure via their complex fractal dimensions, defined as poles of a Lapidus fractal zeta function at infinity. We adapt Minkowski content/dimension at infinity using so-called ϕ\phiϕ-shells and show that the upper ϕ\phiϕ-shell Minkowski dimension is independent of ϕ\phiϕ. Connections with one-point compactification are discussed, and constructions of maximally hyperfractal and quasiperiodic domains at infinity are provided. 
• Journal/Conference: The Journal of Geometric Analysis
• Publication Date:

           – arXiv: submitted 10 Dec 2024, last revised 28 Jul 2025 (v2)

        – Journal version: published 01 Aug 2025

• Volume / Article: 35, Article number 298 (2025)
• Keywords / Subjects: Complex dimensions; fractal zeta functions at infinity; Minkowski content/dimension; unbounded domains; one-point compactification; hyperfractal / quasiperiodic domains; Subjects: math.CV, math-ph
• Contact: Goran Radunović (goran.radunovic@math.hr)
• DOI (arXiv): 10.48550/arXiv.2412.07645
• Related DOI (journal version): 10.1007/s12220-025-02140

• Title: Fractal analysis of canard cycles and slow-fast Hopf points in piecewise smooth Liénard equations
• Authors: Renato Huzak; Ansfried Janssens; Otavio Henrique Perez; Goran Radunović
• Abstract: The paper provides a fractal analysis of piecewise smooth (PWS) slow–fast Liénard equations using the Minkowski dimension of one-dimensional orbits generated by slow relation functions. It determines all possible Minkowski-dimension values near PWS slow–fast Hopf points and near bounded balanced crossing canard cycles, studies unbounded canard cycles in PWS classical Liénard equations, and relates trivial Minkowski dimension to (non-)existence and bounds on crossing-type limit cycles.
• Journal/Conference: arXiv preprint
• Publication Date: Submitted 12 Dec 2024 (v1)
• Subjects / MSC: math.DS; MSC 34E15, 34E17, 34C40, 28A80, 28A75
• Keywords: piecewise smooth systems; slow–fast Liénard equations; canard cycles; slow–fast Hopf points; Minkowski (box) dimension; limit cycles; bifurcations
• Contact: Goran Radunović (submitter), (goran.radunovic@math.hr)
• DOI (arXiv): 10.48550/arXiv.2412.09713

• Title: Integrability of polynomial vector fields and a dual problem
• Authors: Tatjana Petek; Valery Romanovski
• Abstract: We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality the case of quadratic vector fields is considered in detail.
• Journal/Conference: arXiv preprint (Nonlinear Sciences > Exactly Solvable and Integrable Systems)
• Publication Date: Submitted 6 Sep 2024; last revised 21 Nov 2024 (v2)
• Keywords: Polynomial system of ODEs; integrability; first order linear PDE; multigraded rings; invariants
• Contact: Valery Romanovski (submitter on arXiv), (valerij.romanovskij@um.si)
• DOI (arXiv): 10.48550/arXiv.2409.04322

• Title: Managing Financial Instability: A Linear Control Approach for A Chaotic Model
• Authors: Orhan Ozgur Aybar; Ilknur Kusbeyzi Aybar
• Abstract: Nonlinear financial models may exhibit oscillations and chaos, yielding volatility in variables such as interest rate, investment demand, and price index. Many studies analyze such dynamics qualitatively, yet fewer demonstrate when simple linear feedback can reliably suppress chaos and what its practical limits are (e.g., partial measurements, uncertainties, and noise). We study a three-state financial model and ask: can linear state-feedback, designed around a nonzero operating point, stabilize the system in a chaotic parameter regime? What are the tuning and robustness considerations? We linearize about a target equilibrium, design full-state feedback via pole placement (PP) and linear quadratic regulation (LQR), and provide Lyapunov-based local stability certificates together with robustness and measurement-noise bounds. We also document an observer-based realization under partial measurements. In simulations, both PP and LQR stabilize the system locally; LQR converges faster but demands higher peak control effort. An observer-based controller with only one measured state accurately estimates the states but fails to stabilize the nonlinear plant at the intended equilibrium, highlighting limits of linear separation in this setting. In this study, we provide a concise design/tuning recipe for PP and LQR around a nonzero operating point, a constructive Lyapunov-based stability analysis and a practical procedure to estimate the region of attraction, the robustness and ISS bounds, and an explicit demonstration of an observer-based limitation in the nonlinear regime.
• Journal/Conference: International Journal of Applied and Computational Mathematics
• Publication Date: 01 September 2025
• Volume: 11
• Article number: 196
• Keywords: Nonlinear financial system; Chaos control; State feedback control; Pole placement; LQR; Observer-based control; Stabilization; Economic dynamics
• Contact (corresponding author): Orhan Ozgur Aybar, (oaybar@pirireis.edu.tr)
• DOI: 10.1007/s40819-025-02020-7

• Title: Oscillatory dynamics in the adaptive exponential integrate-and-fire model
• Authors: İlknur Kusbeyzi Aybar; Fatma Kocaman; Mert Can Turkmen; Yavuz Yavuz; Bayram Yilmaz; Ahmet Arif Ergin
• Abstract: The paper derives closed-form analytical results for local oscillations in the adaptive exponential integrate-and-fire (AdEx) model. Using rescaling and polynomial approximations of the exponential term, the authors obtain explicit Hopf bifurcation loci and stability criteria, closed-form first Lyapunov coefficients (sub/supercritical; type-I/type-II excitability), and leading-order period coefficients near bifurcation. They also discuss regime transitions (mono-/tri-equilibria) and validate the analytical predictions against the full model, including an application to parameter fitting for AgRP neuron recordings.
• Journal/Conference: Chaos: An Interdisciplinary Journal of Nonlinear Science
• Publication Date: December 1, 2025
• Volume: 35(12)
• Article/Pages: 123–130
• Keywords: adaptive exponential integrate-and-fire (AdEx); Hopf bifurcation; first Lyapunov coefficient; oscillation period coefficients; neural excitability; nonlinear dynamics; parameter fitting; AgRP neurons
• Contact (corresponding author): İlknur Kusbeyzi Aybar, ikusbeyzi@yeditepe.edu.tr
• Doi: 10.1063/5.0301784

• Title: On computations of Poincaré–Dulac normal forms
• Authors: Tatjana Petek, Valery G. Romanovski
• Abstract: There are two approaches to computing Poincaré–Dulac normal forms of systems of ODEs. Under the original approach used by Poincaré and Dulac the normalizing transformation is explicitly computed. On each step, the normalizing procedure requires the substitution of a polynomial into a series. Under the other approach, a normal form is computed using Lie transformations. In this case, the changes of coordinates are performed as actions of certain infinitesimal generators. In both cases, on each step the homological equation is solved in the vector space of polynomial vector fields Vjn\mathcal{V}^n_jVjn​, where each component of the vector field is a homogeneous polynomial of degree j. We present a novel approach which leads to two new algorithms for normal form computations. The first one is designed for polynomial systems of ODEs in which the coefficients of all terms are treated as parameters. While our method employs Lie transformations, the homological equation is solved not in Vjn\mathcal{V}^n_jVjn​ but in the vector space of polynomial vector fields where each component is a homogeneous polynomial in the parameters of the system. It is shown that the space of the parameters is a kind of dual space and the computation of normal forms can be performed in the space of parameters treated as the space of generalized vector fields, which we call the lattice vector fields. The second algorithm applies to any analytic or formal autonomous system of ODEs and offers one of the simplest normal form computation methods available in the literature. Remarkably, the procedure involves only arithmetic operations with scalars, significantly simplifying the computational process.
• Journal/Conference: Journal of Differential Equations
• Publication Date: Available online 8 September 2025
• Volume: 452 (2026), Article 113781
• Keywords: Poincaré–Dulac normal form; Lie transform; Lie algebra of vector fields
• Contact: Valery G. Romanovski  (valerij.romanovskij@um.si)
• DOI: https://doi.org/10.1016/j.jde.2025.113781

• Title: Convergence of normalizations for partially integrable differential systems
• Authors: Wenyong Huang, Valery G. Romanovski, Xiang Zhang
• Abstract: This paper provides some criteria to characterize convergence of normalizations which trans-form partially integrable analytic differential systems to their Poincaré–Dulac normal forms. For a family of four-dimensional partially integrable differential systems near an equilibrium which has one pair of conjugate imaginary eigenvalues and a pair of resonant nonzero real eigenvalues, we prove convergence of their normalizations. For analytic differential systems with dimension larger than 4, we illustrate that partial integrability may not be sufficient to ensure convergence of the normalizations even though Bruno’s condition 𝜔 holds. This work generalizes in a natural way the classical results by Poincaré and Lyapunov for a monodromic equilibrium, as well as the one by Moser for a hyperbolic saddle of analytic Hamiltonian systems of one degree of freedom.
• Journal/Conference: Nonlinear Analysis: Theory, Methods & Applications (TMA)
• Publication Date: 6 August 2025 (online)
• Volume: 262 (2026), Article 113902
• Keywords: analytic differential systems; normal forms; convergence of normalization; first integrals; resonance
• Contact: Valery G. Romanovski (valerij.romanovskij@um.si)
• DOI: https://doi.org/10.1016/j.na.2025.113902

• Title: Modeling the Error of Caliper Measurements in Animal Experiments
• Authors: Melánia Puskás, Dániel András Drexler
• Abstract: Cancer prevention and treatment is one of the most significant public health challenges of
  the 21st century. Cancer is a serious health problem, and it is the second leading cause of death following
  cardiovascular diseases. This requires a reliable virtual patient model, which is usually created based on
  animal studies that precede human studies. Preclinical drug testing often involves mouse experiments, where
  tumors are implanted under the skin. Up until now, the most widespread tumor measurement method is
  caliper measurement, which involves a large measurement error, especially if the tumor is small. We present
  a noise model that can be used to model the measurement noise in animal experiments where tumor size
  is measured with calipers. Accurate in silico measurement is essential, as animal studies are costly, timeconsuming, and strictly regulated. By incorporating a noise model, in silico experiments can better reflect
  real-world measurement uncertainties, improving experimental reproducibility and the reliability of virtual
  patient modeling. In order to model the noise, we use data from preclinical experiments measured using
  MRI and digital calipers, and we use a nonlinear transformation to whiten the noise. Finally, based on the
  Anderson-Darling test, we find the distributions that fit the noise best. We show that virtually generated
  measurements based on the noise model produce similar results to the original measurement noise, thus
  the noise model can be used to create virtual patients and model realistic experimental setups for in silico
  experiments.
• Journal/Conference: IEEE Access
• Publication Date: March 2025
• Volume: 13
• Keywords: Cancer, digital caliper, MRI, measurement error, personalized therapy, preclinical
  experiments, tumor model.
• Contact: Melánia Puskás (puskas.melania@uni-obuda.hu)
• Doi: 10.1109/ACCESS.2025.3555148

• Title: Stability and bifurcations in an epidemic model with nonlinear transmission and removal rates
• Authors: RALUCA EFREM, MIHAELA STERPU, AND DANA CONSTANTINESCU
• Abstract: A generalized SEIR epidemiological model, incorporating general nonlinear transmission and removal rates, has been developed and investigated. Local and global stability theory and bifurcation theory are used to determine the dynamics of the model. The presence of unique or coexisting attractors is proved and different scenarios for the evolution of the model, towards a stable equilibrium point or a limit cycle are found. The theoretical results are supported by numerical simulations, obtained using Holling type II functions.
• Journal/Conference: CARPATHIANJ.MATH
• Publication Date: October 2024
• Volume: 41
• Keywords: SEIR model, stability, bifurcation, nonlinear transmission rate, nonlinear removal rate.
• Contact: Raluca Efrem, raluca.efrem@edu.ucv.ro
• Doi: 10.37193/CJM.2025.02.05

• Title: Local dynamics and bifurcation for a two-dimensional cubic Lotka-Volterra system (Part II)
• Authors: Mihaela Sterpu, Raluca Efrem
• Abstract: The local bifurcation and dynamics for a two-dimensional cubic Kolmogorov system, depending on two small parameters, in certain hypotheses on the coefficients, are investigated. The paper continues the study performed in [4], by treating two non-generic cases, corresponding to the hypotheses that one of the significant coefficients vanishes. In the first non-generic case, the local dynamics is found to be similar to the one obtained in the generic case treated in [4]. In the second non-generic case new possibilities of behavior are found.
• Journal/Conference: Annals of the University of Craiova, Mathematics and Computer Science Series
• Publication Date: December 2024
• Volume: 51(2)
• Keywords: Lotka-Volterra, cubic polynomial system, local bifurcation
• Contact: Mihaela Sterpu, msterpu@inf.ucv.ro
• Doi: 10.52846/ami.v51i2.2070

• Title: Symbolic solution of systems of polynomial differential equations via the Cauchy–Riemann equation: Applications to kinetic differential equations
• Authors: Kelvin Kiprono, János Tóth
• Abstract: The differential equations of chemical kinetics are systems of nonlinear (polynomial) differential equations, therefore their solutions cannot usually be found in symbolic form. Here we offer a method to solve classes of kinetic differential equations based on the Cauchy–Riemann equations. It turns out that the method can be used to symbolically solve some polynomial differential equations that are not necessarily kinetic, as well.
• Journal/Conference: Journal of Mathematical Physics
• Publication Date: April 2025
• Volume: 66
• Keywords: Multivariable calculus, Functions and functionals, Reaction-diffusion system, Symbolic computation, Complex analysis, Complex functions, Reaction rate constants, Chemical kinetics and dynamics
• Contact: János Tóth,  jtoth@math.bme.hu
• Doi: 10.1063/5.0204645

• Title: Reading multiplicity in unfoldings from ε-neighborhoods of orbits
• Authors: RENATO HUZAK, PAVAO MARDEŠIĆ, MAJA RESMAN, VESNA ŽUPANOVIĆ
• Abstract: We consider generic analytic 1-parameter unfoldings of saddle-node germs of analytic vector fields on the real line, their time-one maps and the Lebesgue measure of ε- neighborhoods of the orbits of these time-one maps. The box dimension of an orbit gives the asymptotics of the principal term of this Lebesgue measure and it is known that it is discontinuous at bifurcation parameters. To recover continuous dependence of the asymptotics on the parameter, here we expand asymptotically the Lebesgue measure of ε-neighborhoods of orbits of time-one maps in a Chebyshev system, uniformly with respect to the bifurcation parameter. We use ´Ecalle-Roussarie-type compensators. We show how the number of fixed points of the time-one map born in the universal analytic unfolding of the parabolic point corresponds to the number of terms vanishing in this uniform expansion of the Lebesgue measure of ε-neighborhoods of orbits.
• Journal/Conference: Electronic Journal of Differential Equations
• Publication Date: June 10, 2025
• Volume: 2025 (2025), No. 61
• Keywords: Unfoldings; epsilon-neighborhoods; compensators; Chebyshev scale
• Contact:  Vesna Županović, vesna.zupanovic@fer.unizg.hr
• Doi: 10.58997/ejde.2025.61

• Title: Infinitesimal and tangential 16-th Hilbert problem on zerocycles
• Authors: J.L. Bravo, P. Mardešić, D. Novikov, J. Pontigo-Herrera
• Abstract: In this paper, given two polynomials f and g of one variable and a 0-cycle C of f, we consider the deformation. We define two functions: the displacement function  and its first order approximation: the abelian integral The infinitesimal and tangential 16-th Hilbert problem for zero-cycles are problems of counting isolated regular zeros of for ϵ small, or of , respectively. We show that the two problems are not equivalent and find optimal bounds, in function of the degrees of f and g, for the infinitesimal and tangential 16-th Hilbert problem on zero-cycles. These two problems are the zero-dimensional analog of the classical infinitesimal and tangential 16-th Hilbert problems for vector fields in the plane.
• Journal/Conference: Bulletin des Sciences Mathématiques
• Publication Date: June 2025
• Volume: 202
• Keywords: Infinitesimal and tangential 16-th Hilbert problem; Abelian integrals; Chebyshev property; Deformation of integrable systems
• Contact:  J. Pontigo-Herrera, pontigo@matem.unam.mx
• Doi: 10.1016/j.bulsci.2025.103634