S Li, C Wang, K Wu - Applied Mathematics Letters, 2021 - Elsevier
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 …
L Zhao, J Shen - Discrete and Continuous Dynamical Systems-B, 2022 - aimsciences.org
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 …
R Cai, Y Cai, J Shen - … in Nonlinear Science and Numerical Simulation, 2023 - Elsevier
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 …
TH Hsu, S Ruan - SIAM Journal on Mathematical Analysis, 2021 - SIAM
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 …
Y Wu, M Ni - Chaos, Solitons & Fractals, 2024 - Elsevier
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 …
X Wu, M Ni - Nonlinear Analysis: Modelling and Control, 2022 - zurnalai.vu.lt
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 …
X Ma, H Zhao, Q Bi - Nonlinear Dynamics, 2022 - Springer
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 …