Author(s)

Shuangte Wang¹, Hengguo Yu^1,2, Chuanjun Dai^2,3, Min Zhao^2,3

¹College of Mathematics and Physics, Wenzhou University, Wenzhou, China.
²Key Laboratory for Subtropical Oceans & Lakes Environment & Biological Resources Utilization Technology of Zhejiang, Wenzhou University, Wenzhou, China.
³School of Life and Environmental Science, Wenzhou University, Wenzhou, China.

In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.

Predator-Prey System, Holling Type II Functional Response, Global Stability, Bifurcation Analysis

Wang, S. , Yu, H. , Dai, C. and Zhao, M. (2020) The Dynamical Behavior of a Certain Predator-Prey System with Holling Type II Functional Response. Journal of Applied Mathematics and Physics, 8, 527-547. doi: 10.4236/jamp.2020.83042.