Bifurcation analysis and chaos control in a host‐parasitoid model

Abstract

We investigate the qualitative behavior of a host‐parasitoid model with a strong Allee effect on the host. More precisely, we discuss the boundedness, existence and uniqueness of positive equilibrium, local asymptotic stability of positive equilibrium and existence of Neimark–Sacker bifurcation for the given system by using bifurcation theory. In order to control Neimark–Sacker bifurcation, we apply pole‐placement technique that is a modification of OGY method. Moreover, the hybrid control methodology is implemented in order to control Neimark–Sacker bifurcation. Numerical simulations are provided to illustrate theoretical discussion. Copyright © 2017 John Wiley & Sons, Ltd.

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

“…In this section, we want to investigate the conditions for existence and direction of Neimark-Sacker bifurcation at positive equilibrium point of system (5). For a similar type of discussion related to the existence and direction of Neimark-Sacker bifurcation, we refer the interested reader to [1,23,24,28,[32][33][34][35][36][39][40][41] and references therein. Notice that, the roots of characteristic polynomial (16) are conjugate complex numbers if the following condition is satisfied:…”

“…In this section, we study two feedback control strategies in order to move the unstable trajectory towards the stable one. For similar types of investigations we refer to [1,[32][33][34][35][36][37][38][39][40][41] for controlling chaos in discrete-time population models. For some other applications related to chaos control, see also [51][52][53][54][55][56][57][58][59][60][61][62].…”

“…In [1,[20][21][22][23][24], the parametric conditions for global behavior of host-parasitoid models are investigated. Recently, in [1,23,24,32,33,35], the parametric conditions for existence and direction of Neimark-Sacker bifurcation are investigated, and in [1,32,33,35] feedback chaos control strategies are implemented for controlling chaos and bifurcations in host-parasitoid models. Moreover, for state-feedback control design based on the matrix inequality approaches, we refer to [63][64][65][66].…”

Stability of a certain class of a host–parasitoid models with a spatial refuge effect

“…Many authors have investigated different types of discrete host-parasitoid models under different ecological factors and different assumptions, see for example [1,7,[12][13][14][18][19][20][21]23,24,28].…”

Neimark–Sacker bifurcation and stability analysis of a discrete-time prey–predator model with Allee effect in prey

“…The analysis of bifurcations has already received much attention during the last few years [20,[22][23][24][25][26][27][28][29]. Bifurcation and stability analysis are examined in detail in [20,[22][23][24][30][31][32][33][34][35][36][37][38][39][40][41].…”