Bifurcation analysis and chaos control in a discrete‐time plant quality and larch budmoth interaction model with Ricker equation

Abstract

We investigate the dynamics of two‐dimensional discrete‐time model of leaf quality and larch budmoth interaction with Ricker equation. More precisely, the qualitative behavior of larch budmoth model is discussed in which the effect of food source upon the moth population is through intrinsic growth rate. We find the parametric conditions for local asymptotic stability of the unique positive fixed point. It is also proved that under certain parametric conditions, the system undergoes period‐doubling bifurcation with the help of center manifold theory. The parametric conditions for existence and direction of Neimark‐Sacker bifurcation at positive fixed point is investigated with the help of standard mathematical techniques of bifurcation theory. The chaos control in the system is discussed through implementation of hybrid control methodology. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long‐term behavior over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the system.