Volume 34, Issue 2
Dynamics of a Predator-Prey Reaction-Diffusion System with Non-Monotonic Functional Response Function

Huan Wang & Cunhua Zhang

Ann. Appl. Math., 34 (2018), pp. 199-220.

Published online: 2022-06

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  • Abstract

In this article, a two-species predator-prey reaction-diffusion system with Holling type-IV functional response and subject to the homogeneous Neumann boundary condition is regarded. In the absence of the spatial diffusion, the local asymptotic stability, the instability and the existence of Hopf bifurcation of the positive equilibria of the corresponding local system are analyzed in detail by means of the basic theory for dynamical systems. As well, the effect of the spatial diffusion on the stability of the positive equilibria is considered by using the linearized method and analyzing in detail the distribution of roots in the complex plane of the associated eigenvalue problem. In order to verify the obtained theoretical predictions, some examples and numerical simulations are also included by applying the numerical methods to solve the ordinary and partial differential equations.

  • AMS Subject Headings

35B35, 35B40, 35K57, 92D40

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COPYRIGHT: © Global Science Press

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@Article{AAM-34-199, author = {Wang , Huan and Zhang , Cunhua}, title = {Dynamics of a Predator-Prey Reaction-Diffusion System with Non-Monotonic Functional Response Function}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {34}, number = {2}, pages = {199--220}, abstract = {

In this article, a two-species predator-prey reaction-diffusion system with Holling type-IV functional response and subject to the homogeneous Neumann boundary condition is regarded. In the absence of the spatial diffusion, the local asymptotic stability, the instability and the existence of Hopf bifurcation of the positive equilibria of the corresponding local system are analyzed in detail by means of the basic theory for dynamical systems. As well, the effect of the spatial diffusion on the stability of the positive equilibria is considered by using the linearized method and analyzing in detail the distribution of roots in the complex plane of the associated eigenvalue problem. In order to verify the obtained theoretical predictions, some examples and numerical simulations are also included by applying the numerical methods to solve the ordinary and partial differential equations.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20573.html} }
TY - JOUR T1 - Dynamics of a Predator-Prey Reaction-Diffusion System with Non-Monotonic Functional Response Function AU - Wang , Huan AU - Zhang , Cunhua JO - Annals of Applied Mathematics VL - 2 SP - 199 EP - 220 PY - 2022 DA - 2022/06 SN - 34 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20573.html KW - reaction-diffusion system, predator-prey system, asymptotic stability, Hopf bifurcation. AB -

In this article, a two-species predator-prey reaction-diffusion system with Holling type-IV functional response and subject to the homogeneous Neumann boundary condition is regarded. In the absence of the spatial diffusion, the local asymptotic stability, the instability and the existence of Hopf bifurcation of the positive equilibria of the corresponding local system are analyzed in detail by means of the basic theory for dynamical systems. As well, the effect of the spatial diffusion on the stability of the positive equilibria is considered by using the linearized method and analyzing in detail the distribution of roots in the complex plane of the associated eigenvalue problem. In order to verify the obtained theoretical predictions, some examples and numerical simulations are also included by applying the numerical methods to solve the ordinary and partial differential equations.

Wang , Huan and Zhang , Cunhua. (2022). Dynamics of a Predator-Prey Reaction-Diffusion System with Non-Monotonic Functional Response Function. Annals of Applied Mathematics. 34 (2). 199-220. doi:
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