Open AccessStability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response
Author(s) -
Shuangte Wang,
Hengguo Yu
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021391
Subject(s) - hopf bifurcation , functional response , bifurcation , mathematics , predation , predator , limit cycle , stability (learning theory) , bifurcation theory , control theory (sociology) , biological applications of bifurcation theory , limit (mathematics) , ecology , mathematical analysis , computer science , physics , biology , nonlinear system , artificial intelligence , control (management) , quantum mechanics , machine learning
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.