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Volume 31, Issue 4
Dynamics of a Delayed Predator-Prey System with Stage Structure for Predator and Prey

Juan Liu & Zizhen Zhang

DOI: 10.13447/j.1674-5647.2015.04.02

Commun. Math. Res., 31 (2015), pp. 298-310.

Published online: 2021-05

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  • Abstract

In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally, numerical simulations are presented to support the theoretical analysis.

  • Keywords

time delay, stage-structure, Hopf bifurcation, stability, periodic solution.

  • AMS Subject Headings

34C05, 34D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-298, author = {Liu , Juan and Zhang , Zizhen}, title = {Dynamics of a Delayed Predator-Prey System with Stage Structure for Predator and Prey}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {4}, pages = {298--310}, abstract = {

In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally, numerical simulations are presented to support the theoretical analysis.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.02}, url = {http://global-sci.org/intro/article_detail/cmr/18912.html} }
TY - JOUR T1 - Dynamics of a Delayed Predator-Prey System with Stage Structure for Predator and Prey AU - Liu , Juan AU - Zhang , Zizhen JO - Communications in Mathematical Research VL - 4 SP - 298 EP - 310 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.04.02 UR - https://global-sci.org/intro/article_detail/cmr/18912.html KW - time delay, stage-structure, Hopf bifurcation, stability, periodic solution. AB -

In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally, numerical simulations are presented to support the theoretical analysis.

Liu , Juan and Zhang , Zizhen. (2021). Dynamics of a Delayed Predator-Prey System with Stage Structure for Predator and Prey. Communications in Mathematical Research . 31 (4). 298-310. doi:10.13447/j.1674-5647.2015.04.02
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