Revisit a SIR System: Using the Dynamical System Approach to Detect Slow-Fast Oscillations

Simulating Stochastic Population Dynamics: The Linear Noise Approximation Can Capture Nonlinear Phenomena

A new framework based on center manifold theory is introduced, a classical concept from nonlinear dynamical systems, that enables the identification of simple, system-specific modifications to the LNA, tailored to classes of qualitatively similar nonlinear dynamical systems.

Dynamics and Strong Resonance Bifurcations in a Discrete Predator–Prey Model With Square Root Functional Response

This paper investigates the dynamic behavior of a discrete‐time predator–prey model incorporating a square root functional response, which captures the herding behavior of prey populations. By applying Euler discretization to the continuous‐time model, we obtain a system of difference equations that serves as the fou...

A robust and efficient iterative approach for unified computation of Lyapunov–Perron transformation and characteristic exponents

Stability Analysis of a Discrete Dynamical System With Density Dependence and Mutual Interference

To address the limitations of classical fishery population models (e.g., Ricker and Beverton–Holt) in capturing complex interspecific interactions and lag effects, this article constructs an improved two‐species, discrete dynamic model, y n + 1 = a y n 1 + p z n e − y n , z n + 1 = b z n 1 + q y n e − z n $$ {y}_{n+1}=...

Chaos and Bifurcation Analysis of a Discrete Time Financial Risk Model

Financial risk dynamics often exhibit irregular fluctuations that are well described by nonlinear models with complex behavior. Motivated by the suitability of discrete-time representations for financial phenomena, this paper develops and studies a discrete-time financial risk evolution model obtained by applying the f...

Dynamical analysis, bifurcations and slow-fast behavior of a predator-prey model with hunting cooperation

The main focus of this paper is to investigate the dynamical behaviors of a predator-prey model incorporating cooperative hunting among predators, which is widely observed in real ecological communities and provides valuable insights for revealing population persistence and community stability in natural ecosystems.