Saddle-node bifurcation

Statistics

Functional response

Physics

Paleontology

Artificial intelligence

Nonlinear system

Hopf bifurcation

Biological applications of bifurcation theory

Predation

Ecology

Control (management)

Type (biology)

Bifurcation

Applied mathematics

Mathematics

Computer science

Control theory (sociology)

Transcritical bifurcation

Discrete time and continuous time

Quantum mechanics

Center manifold

Biology

Predator

Journal of Computational and Applied Mathematics

In this paper, we study the complex dynamical behavior in a discrete prey–predator model with Holling type II functional response with prey refuge. It is exhibited that the system shows different types of bifurcations viz. flip bifurcation, transcritical bifurcation and Neimark–Sacker bifurcation(NSB) by using center manifold theorem and bifurcation theory. Moreover, the chaos occurred in the system has been controlled by deploying control strategies viz. state feedback, pole placement and hybrid control techniques. The certain conditions have been determined under which chaos and bifurcation can be stabilized. The extensive numerical simulation is performed to demonstrate the analytical findings.

Bifurcations and chaos control in a discrete-time prey–predator model with Holling type-II functional response and prey refuge