Bifurcation analysis and hybrid control of a discrete-time predator–prey model

Abstract

In this paper, a discrete-time predator–prey model with six parameters is investigated. After splitting the parameter space with respect to the number of fixed points, we obtain both transcritical bifurcation surfaces and a Neimark–Sacker bifurcation surface in the six-dimensional parameter space by the normal form method. Then we apply a hybrid control strategy to control the Neimark–Sacker bifurcation so that the positive fixed point of the controlled system is locally asymptotically stable. Numerical simulations are performed to illustrate our theoretical results.

Keywords:

• Hybrid control
• Neimark–Sacker bifurcation
• predator–prey model
• transcritical bifurcation

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34C23
• 34H20
• 37G15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by NSFC #11871355.