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Review Open access Sep 2026

Oscillations in Dynamic Models of the Wilson-Cowan Type System

A review of samples of oscillations in a system of ordinary differential equations that arise in mathematical models of complex networks is provided. Starting from the low-dimensional systems, we go up in the sense of system dimensionality, commenting on various patterns that appear. We overlook examples of relatively...

F. Sadyrbaev, V. Sengileyev · 0 citations
Open access Sep 2026

A Population Model with Smooth Functions and Application

The purpose of this paper is to give sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain \(\Omega\) in \(R^{n}\). Also considered are the effects of perturbations on the coexistence state and uniqueness. Th...

J. H. Kang · 0 citations
Preprint Sep 2026

Fitness, predictability and equilibrium in biological dynamics

Understanding eco-evolutionary dynamics presents significant mathematical challenges, particularly regarding predictability, equilibrium, and the mathematical representation of fitness. Using Open System Dynamics and Stochastic Analysis, we develop a theoretical framework to characterize fitness change and its relation...

Rolando Rebolledo, Mauricio Tejo, M. Freilich et al. · 0 citations
Sep 2026

Bifurcation Analysis on a Diffusive Minimal Model of Plankton Systems with Stage Structure

In this study, we investigate the dynamics of a diffusive minimal plankton model with stage structure. We first establish sufficient conditions for the existence of a unique positive constant steady state. Building on this, we analyze the stability of the equilibrium and examine potential Hopf bifurcations and Turing b...

Qian-Qian Sun, Chun-Jin Wei, Jun-Jie Wei · 0 citations
Open access Sep 2026

Temperature-Structured PDE Model for Population Dynamics

This paper proposes a population model structured by temperature, in which thermal variation is incorporated directly as a continuous internal variable rather than treated as an external input. The resulting formulation leads to a non-linear parabolic partial differential equation that includes diffusion along the temp...

Alphy Joseph, K. Ashok, Fijy Jose P · 0 citations
Preprint Sep 2026

Linear Response Theory for Jump-Driven Stochastic Systems: Transient Statistics and Escape Dynamics

In this paper, we develop a linear response theory for a class of stochastic differential equations driven by jump processes. We investigate the response of the system to small time-dependent perturbations from three complementary perspectives: probability density functions, mean exit times, and escape probabilities. B...

Qing-Yan Meng, Jin-Qiao Duan, V. Lucarini · 0 citations

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