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Volume 10, Issue 1
Hopf Bifurcation and Singularity Induced Bifurcation in a Leslie-Gower Predator-Prey System with Nonlinear Harvesting

Wei Liu & Yaolin Jiang

DOI: 10.4208/eajam.030519.110719

East Asian J. Appl. Math., 10 (2020), pp. 181-216.

Published online: 2020-01

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  • Abstract

A modified predator-prey model with a new nonlinear harvesting on predator and gestation delay of prey is studied. It is shown that the stability of interior equilibrium point can switch finite times and Hopf bifurcations occur when delay increases through critical values. The properties of the Hopf bifurcations are investigated by the center manifold theorem. Special attention is paid to singularity-induced bifurcations and their state feedback control. Numerical simulations demonstrate the effectiveness of the theoretical results.

  • Keywords

Predator-prey, nonlinear harvesting, delay, Hopf bifurcation, singularity-induced bifurcation.

  • AMS Subject Headings

34D20, 34C23, 34C25, 92D25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wliu2015@163.com (Wei Liu)

yljiang@xjtu.edu.cn (Yaolin Jiang)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-181, author = {Liu , Wei and Jiang , Yaolin}, title = {Hopf Bifurcation and Singularity Induced Bifurcation in a Leslie-Gower Predator-Prey System with Nonlinear Harvesting}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {1}, pages = {181--216}, abstract = {

A modified predator-prey model with a new nonlinear harvesting on predator and gestation delay of prey is studied. It is shown that the stability of interior equilibrium point can switch finite times and Hopf bifurcations occur when delay increases through critical values. The properties of the Hopf bifurcations are investigated by the center manifold theorem. Special attention is paid to singularity-induced bifurcations and their state feedback control. Numerical simulations demonstrate the effectiveness of the theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.030519.110719}, url = {http://global-sci.org/intro/article_detail/eajam/13609.html} }
TY - JOUR T1 - Hopf Bifurcation and Singularity Induced Bifurcation in a Leslie-Gower Predator-Prey System with Nonlinear Harvesting AU - Liu , Wei AU - Jiang , Yaolin JO - East Asian Journal on Applied Mathematics VL - 1 SP - 181 EP - 216 PY - 2020 DA - 2020/01 SN - 10 DO - http://doi.org/10.4208/eajam.030519.110719 UR - https://global-sci.org/intro/article_detail/eajam/13609.html KW - Predator-prey, nonlinear harvesting, delay, Hopf bifurcation, singularity-induced bifurcation. AB -

A modified predator-prey model with a new nonlinear harvesting on predator and gestation delay of prey is studied. It is shown that the stability of interior equilibrium point can switch finite times and Hopf bifurcations occur when delay increases through critical values. The properties of the Hopf bifurcations are investigated by the center manifold theorem. Special attention is paid to singularity-induced bifurcations and their state feedback control. Numerical simulations demonstrate the effectiveness of the theoretical results.

Liu , Wei and Jiang , Yaolin. (2020). Hopf Bifurcation and Singularity Induced Bifurcation in a Leslie-Gower Predator-Prey System with Nonlinear Harvesting. East Asian Journal on Applied Mathematics. 10 (1). 181-216. doi:10.4208/eajam.030519.110719
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