Relaxation oscillations and canard explosion in a predator-prey system of Holling and Leslie types

DOI10.1016/j.nonrwa.2017.01.006zbMath1362.34074OpenAlexW2581883118MaRDI QIDQ518731

Ali Atabaigi, Ali Barati

Publication date: 30 March 2017

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2017.01.006

zbMATH Keywords

relaxation oscillationspredator-prey systemgeometric singular perturbation theorycanard explosionHolling and Leslie

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Qualitative investigation and simulation of ordinary differential equation models (34C60) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26) Canard solutions to ordinary differential equations (34E17)

Related Items (16)

Relaxation Oscillations and Canard Explosion of a Leslie–Gower Predator–Prey System with Addictive Allee Effect ⋮ Dynamics in diffusive Leslie–Gower prey–predator model with weak diffusion ⋮ Canard Cycles and Relaxation Oscillations in a Singularly Perturbed Leslie–Gower Predator–Prey Model with Allee Effect ⋮ Relaxation oscillations in a slow-fast predator-prey model with weak Allee effect and Holling-IV functional response ⋮ Existence of traveling wave solutions in a singularly perturbed predator-prey equation with spatial diffusion ⋮ Relaxation oscillation and canard explosion in a slow-fast predator-prey model with Beddington-DeAngelis functional response ⋮ High-Order Analysis of Canard Explosion in the Brusselator Equations ⋮ Relaxation oscillations and dynamical properties in two time-delay slow-fast modified Leslie-Gower models ⋮ Relaxation oscillations for Leslie-type predator-prey model with Holling type I response functional function ⋮ A novel strategy of bifurcation control for a delayed fractional predator-prey model ⋮ The entry-exit theorem and relaxation oscillations in slow-fast planar systems ⋮ Canard explosion, homoclinic and heteroclinic orbits in singularly perturbed generalist predator–prey systems ⋮ Bifurcation Analysis of a Diffusive Predator–Prey Model with Monod–Haldane Functional Response ⋮ Asymptotic expansions for a degenerate canard explosion ⋮ Canards and homoclinic orbits in a slow-fast modified May-Holling-Tanner predator-prey model with weak multiple allee effect ⋮ Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method

Cites Work

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• Uniqueness of limit cycles in Gause-type models of predator-prey systems
• Geometric singular perturbation theory for ordinary differential equations
• Relaxation oscillations in a class of predator-prey systems.
• Bifurcations in a predator-prey system of Leslie type with generalized Holling type III functional response
• Bifurcations of a predator-prey system of Holling and Leslie types
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• Canard-like phenomena in piecewise-smooth Van der Pol systems
• More limit cycles than expected in Liénard equations
• Canard cycles and center manifolds
• Travelling waves in the Holling–Tanner model with weak diffusion
• Relaxation oscillation and canard explosion
• The entry-exit function and geometric singular perturbation theory

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