Open AccessBifurcation analysis and chaos control of a discrete-time prey-predator model with fear factor
Author(s) -
Ceyu Lei,
Xiaoling Han,
Weiming Wang
Publication year - 2022
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.2022313
Subject(s) - bifurcation , mathematics , saddle node bifurcation , transcritical bifurcation , biological applications of bifurcation theory , center manifold , predator , control theory (sociology) , bifurcation diagram , bifurcation theory , stability (learning theory) , predation , chaos (operating system) , complex dynamics , infinite period bifurcation , homoclinic bifurcation , mathematical analysis , hopf bifurcation , control (management) , computer science , physics , ecology , artificial intelligence , biology , nonlinear system , quantum mechanics , computer security , machine learning
In this paper, we investigate the complex dynamics of a classical discrete-time prey-predator system with the cost of anti-predator behaviors. We first give the existence and stability of fixed points of this system. And by using the central manifold theorem and bifurcation theory, we prove that the system will experience flip bifurcation and Neimark-Sacker bifurcation at the equilibrium points. Furthermore, we illustrate the bifurcation phenomenon and chaos characteristics via numerical simulations. The results may enrich the dynamics of the prey-predator systems.