full
search.png

Search

close.png

Cancel

Volume 6, Issue 4
Canard Phenomenon and Dynamics for a Slow-Fast Leslie-Gower Prey-Predator Model with Monod-Haldane Function Response

Xiao Wu & Mingkang Ni

DOI: 10.12150/jnma.2024.998

J. Nonl. Mod. Anal., 6 (2024), pp. 998-1021.

Published online: 2024-12

[An open-access article; the PDF is free to any online user.]

Preview Full PDF 90 1419

Cited by

google scholar semantic scholar
Export citation
  • Abstract

The geometrical singular perturbation theory has been successfully applied in studying a large range of mathematical biological models with different time scales. In this paper, we use the geometrical singular perturbation theory to investigate a slow-fast Leslie-Gower prey-predator model with Monod-Haldane function response and get some interesting dynamical phenomena such as singular Hopf bifurcation, canard explosion phenomenon, relaxation oscillation cycle, heteroclinic and homoclinic orbits and the coexistence of canard cycle and relaxation oscillation cycle.

  • Keywords

Leslie-Gower prey-predator model, slow-fast system, canard explosion phenomenon, relaxation oscillation cycle, heteroclinic orbit, homoclinic orbit.

  • AMS Subject Headings

34C37, 34C26, 34C07, 37G15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JNMA-6-998, author = {Wu , Xiao and Ni , Mingkang}, title = {Canard Phenomenon and Dynamics for a Slow-Fast Leslie-Gower Prey-Predator Model with Monod-Haldane Function Response}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {4}, pages = {998--1021}, abstract = {

The geometrical singular perturbation theory has been successfully applied in studying a large range of mathematical biological models with different time scales. In this paper, we use the geometrical singular perturbation theory to investigate a slow-fast Leslie-Gower prey-predator model with Monod-Haldane function response and get some interesting dynamical phenomena such as singular Hopf bifurcation, canard explosion phenomenon, relaxation oscillation cycle, heteroclinic and homoclinic orbits and the coexistence of canard cycle and relaxation oscillation cycle.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.998}, url = {http://global-sci.org/intro/article_detail/jnma/23668.html} }
TY - JOUR T1 - Canard Phenomenon and Dynamics for a Slow-Fast Leslie-Gower Prey-Predator Model with Monod-Haldane Function Response AU - Wu , Xiao AU - Ni , Mingkang JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 998 EP - 1021 PY - 2024 DA - 2024/12 SN - 6 DO - http://doi.org/10.12150/jnma.2024.998 UR - https://global-sci.org/intro/article_detail/jnma/23668.html KW - Leslie-Gower prey-predator model, slow-fast system, canard explosion phenomenon, relaxation oscillation cycle, heteroclinic orbit, homoclinic orbit. AB -

The geometrical singular perturbation theory has been successfully applied in studying a large range of mathematical biological models with different time scales. In this paper, we use the geometrical singular perturbation theory to investigate a slow-fast Leslie-Gower prey-predator model with Monod-Haldane function response and get some interesting dynamical phenomena such as singular Hopf bifurcation, canard explosion phenomenon, relaxation oscillation cycle, heteroclinic and homoclinic orbits and the coexistence of canard cycle and relaxation oscillation cycle.

Wu , Xiao and Ni , Mingkang. (2024). Canard Phenomenon and Dynamics for a Slow-Fast Leslie-Gower Prey-Predator Model with Monod-Haldane Function Response. Journal of Nonlinear Modeling and Analysis. 6 (4). 998-1021. doi:10.12150/jnma.2024.998
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard