Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response

In the paper, stability and bifurcation behaviors of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response are studied theoretically and numerically. Mathematical theory works mainly give some critical threshold conditions to guarantee the existence and stability of all...

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Autores principales:	Shuangte Wang, Hengguo Yu
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	bazykin's predator-prey ecosystem stability hopf bifurcation bogdanov-takens bifurcation limit cycle Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/029712159c4044f08fb6d1f78abb6dac
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spelling	oai:doaj.org-article:029712159c4044f08fb6d1f78abb6dac2021-11-23T02:54:40ZStability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response10.3934/mbe.20213911551-0018https://doaj.org/article/029712159c4044f08fb6d1f78abb6dac2021-09-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021391?viewType=HTMLhttps://doaj.org/toc/1551-0018In the paper, stability and bifurcation behaviors of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response are studied theoretically and numerically. Mathematical theory works mainly give some critical threshold conditions to guarantee the existence and stability of all possible equilibrium points, and the occurrence of Hopf bifurcation and Bogdanov-Takens bifurcation. Numerical simulation works mainly display that the Bazykin's predator-prey ecosystem has complex dynamic behaviors, which also directly proves that the theoretical results are effective and feasible. Furthermore, it is easy to see from numerical simulation results that some key parameters can seriously affect the dynamic behavior evolution process of the Bazykin's predator-prey ecosystem. Moreover, limit cycle is proposed in view of the supercritical Hopf bifurcation. Finally, it is expected that these results will contribute to the dynamical behaviors of predator-prey ecosystem.Shuangte WangHengguo YuAIMS Pressarticlebazykin's predator-prey ecosystemstabilityhopf bifurcationbogdanov-takens bifurcationlimit cycleBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 6, Pp 7877-7918 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	bazykin's predator-prey ecosystem stability hopf bifurcation bogdanov-takens bifurcation limit cycle Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	bazykin's predator-prey ecosystem stability hopf bifurcation bogdanov-takens bifurcation limit cycle Biotechnology TP248.13-248.65 Mathematics QA1-939 Shuangte Wang Hengguo Yu Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response
description	In the paper, stability and bifurcation behaviors of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response are studied theoretically and numerically. Mathematical theory works mainly give some critical threshold conditions to guarantee the existence and stability of all possible equilibrium points, and the occurrence of Hopf bifurcation and Bogdanov-Takens bifurcation. Numerical simulation works mainly display that the Bazykin's predator-prey ecosystem has complex dynamic behaviors, which also directly proves that the theoretical results are effective and feasible. Furthermore, it is easy to see from numerical simulation results that some key parameters can seriously affect the dynamic behavior evolution process of the Bazykin's predator-prey ecosystem. Moreover, limit cycle is proposed in view of the supercritical Hopf bifurcation. Finally, it is expected that these results will contribute to the dynamical behaviors of predator-prey ecosystem.
format	article
author	Shuangte Wang Hengguo Yu
author_facet	Shuangte Wang Hengguo Yu
author_sort	Shuangte Wang
title	Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response
title_short	Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response
title_full	Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response
title_fullStr	Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response
title_full_unstemmed	Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response
title_sort	stability and bifurcation analysis of the bazykin's predator-prey ecosystem with holling type ⅱ functional response
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/029712159c4044f08fb6d1f78abb6dac
work_keys_str_mv	AT shuangtewang stabilityandbifurcationanalysisofthebazykinspredatorpreyecosystemwithhollingtypeiifunctionalresponse AT hengguoyu stabilityandbifurcationanalysisofthebazykinspredatorpreyecosystemwithhollingtypeiifunctionalresponse
_version_	1718417357553008640

Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response

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