Bifurcation Analysis and Chaos Control in Discrete-Time Non-Linear Dynamical Systems

Abstract

The main objective of this thesis is to investigate the dynamics of two dimensional discrete time model of leaf-quality and larch-budmoth interac tion with Ricker equation, three-dimensional Ricker type discrete-time com petition model and discrete-time four-dimensional predator prey model with parasites. We study the boundedness of solutions, uniqueness, existence and local asymptotic-stability of the unique positive xed point. It is also proved that under certain parametric conditions, the corresponding system under goes period-doubling bifurcation (PDB) by using center-manifold theory and also Neimark-Sacker bifurcation (NSB) occurs for the positive xed point by using methods of bifurcation theory. Bifurcation in higher dimensional systems is also discussed by using an explicit criterion for NSB and PDB. In order to control bifurcation, we apply the hybrid control technique. Nu merical simulations are also provided to illustrate our theoretical results. Computation of maximum Lyapunov exponents and numerical simulations showed chaotic long term behavior over a broad-range of parameters. Keywords: Discrete-time models, Neimark-Sacker bifurcation, larch bud moth population, boundedness, local asymptotic stability, chaos control, period-doubling bifurcation, competition model, predator-prey model.