Neimark-Sacker Bifurcation and Control of Chaotic Behavior in a Discrete-Time Plant-Herbivore System

Abstract

In this study, the dynamics of a discrete-time plant-herbivore model obtained using the forward Euler method are discussed. The existence of fixed points is investigated. A topological classification is made to examine the behavior of the positive fixed point where the plant and the herbivore coexist. In addition, the existence conditions and direction of Neimark-Sacker bifurcation of the model are investigated using bifurcation theory. Hybrid control method is applied to control the chaos caused by Neimark-Sacker bifurcation. Examples including time series figures, bifurcation figures, phase portraits and maximum Lyapunov exponent are provided to support our theoretical results.

Qualitative Analysis of a Nicholson-Bailey Model in Patchy Environment

“…Next, we use a hybrid control technique [22,[30][31][32][33] to control the chaotic behavior of (1.1) at fixed point (H * , P * ) due to Neimark-Sacker bifurcation. We consider the following controlled system associated with the system (1.1):…”