Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

Abstract

In this paper, a new density-dependent host-parasitoid model is proposed. The modification is based on density-dependent factor by introducing Hassell growth function in host population. Moreover, the permanence of solutions, existence and uniqueness of positive equilibrium, local asymptotic stability and global behavior of the positive equilibrium point are also investigated. It is demonstrated that system endures Neimark-Sacker bifurcation for wide range of bifurcation parameter. In order to control chaos due to emergence of Neimark-Sacker bifurcation, two feedback control strategies, that is, OGY and hybrid control methods are implemented. Finally, all mathematical analysis, particularly, Neimark-Sacker bifurcation, chaos control strategies, and global asymptotic stability of unique positive point are verified with the help of numerical simulations.

Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

“…In dynamical systems, it is expected that the system be optimized with respect to some performance criterion and chaos be avoided. Controlling chaos in discrete-time systems is a topic of great interest for many researchers in recent time [5][6][7][8][9].…”

Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response

“…On the other hand, population models with non-overlapping generations have more irregular complex behaviour. For some recent investigation related to chaos control in discrete-time models we refer to [1,[13][14][15][16][17][18][19][20][22][23][24] and references are therein. In this section, first we discuss pole-placement chaos control method based on state feedback control which was introduced by Romeiras et al [44] (also see [41]).…”

A dynamically consistent nonstandard finite difference scheme for a predator–prey model

“…Recently, many iterated maps have been studied for existence and direction of Neimark-Sacker bifurcation (cf. [37][38][39][40][41][42][43][44][45][46][47][48][49][50]).…”