By using geometric singular perturbation theory and a new entry–exit function, this paper is
concerned with the number and stability of relaxation oscillations in a slow–fast predator …

The paper investigates the relaxation oscillations of a classical predator–prey model, based
on the natural ecological assumption that the maximum per capita birth rate of the predator …

This paper studies bifurcations of canards and homoclinic orbits in a slow-fast modified May-
Holling-Tanner predator-prey model with weak multiple Allee effect. Based on geometric …

In this article, we study the coexistence of one predator and two prey with evolutionary
effects. To that end, we formulate a three-time-scale model with rapid adaptive in predator's …

For a slow-fast system of the form ̇p=ϵf(p,z,ϵ)+h(p,z,ϵ), ̇z=g(p,z,ϵ) for
(p,z)∈\mathbbR^n*\mathbbR^m, we consider the scenario that the system has invariant sets …

In this article, we investigate the complex dynamics of the Hastings–Powell model with the
additive Allee effect. Due to the differences of each species at different time scales, we …

This paper is concerned with the diffusive Leslie–Gower prey–predator model with weak
diffusion. Assuming that the diffusion rates of prey and predator are sufficiently small and the …

A three‐species food chain model with Allee and fear effects on both prey and predator is
investigated in this work. The model consists of ODEs describing the evolution and …

The complex bursting dynamics of a mechanical oscillator under parametric and external
forced excitations are investigated. When the frequencies of the forcing terms are much …

We derive characteristic functions to determine the number and stability of relaxation
oscillations for a class of planar systems. Applying our criterion, we give conditions under …