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Volume 4, Issue 2
Analysis of the Dynamics of a Predator-Prey Model with Holling Functional Response

Hongyu Chen & Chunrui Zhang

DOI: 10.12150/jnma.2022.310

J. Nonl. Mod. Anal., 4 (2022), pp. 310-324.

Published online: 2022-06

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

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  • Abstract

A diffusive predator-prey system with Holling functional response is considered. Firstly, existence of positive equilibrium of this reaction diffusion model under Neumann boundary condition is obtained. Meanwhile, the existence conditions for Turing instability and Hopf bifurcations of a system with Holling II functional response are established. Next, the existence of the hydra effect is demonstrated, when the system is undergoing non-homogeneous steady-state solutions. Finally, numerical simulations are illustrated to support our theory results.

  • Keywords

Predator-prey model, Turing instability, Hopf bifurcation, Hydra effect.

  • AMS Subject Headings

34C23, 35K57

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JNMA-4-310, author = {Chen , Hongyu and Zhang , Chunrui}, title = {Analysis of the Dynamics of a Predator-Prey Model with Holling Functional Response}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {2}, pages = {310--324}, abstract = {

A diffusive predator-prey system with Holling functional response is considered. Firstly, existence of positive equilibrium of this reaction diffusion model under Neumann boundary condition is obtained. Meanwhile, the existence conditions for Turing instability and Hopf bifurcations of a system with Holling II functional response are established. Next, the existence of the hydra effect is demonstrated, when the system is undergoing non-homogeneous steady-state solutions. Finally, numerical simulations are illustrated to support our theory results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.310}, url = {http://global-sci.org/intro/article_detail/jnma/20710.html} }
TY - JOUR T1 - Analysis of the Dynamics of a Predator-Prey Model with Holling Functional Response AU - Chen , Hongyu AU - Zhang , Chunrui JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 310 EP - 324 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.310 UR - https://global-sci.org/intro/article_detail/jnma/20710.html KW - Predator-prey model, Turing instability, Hopf bifurcation, Hydra effect. AB -

A diffusive predator-prey system with Holling functional response is considered. Firstly, existence of positive equilibrium of this reaction diffusion model under Neumann boundary condition is obtained. Meanwhile, the existence conditions for Turing instability and Hopf bifurcations of a system with Holling II functional response are established. Next, the existence of the hydra effect is demonstrated, when the system is undergoing non-homogeneous steady-state solutions. Finally, numerical simulations are illustrated to support our theory results.

Hongyu Chen & Chunrui Zhang. (2022). Analysis of the Dynamics of a Predator-Prey Model with Holling Functional Response. Journal of Nonlinear Modeling and Analysis. 4 (2). 310-324. doi:10.12150/jnma.2022.310
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