Bifurcation analysis and chaos control in discrete-time system of three competing species

Abstract

In this paper, we investigate the complex dynamics of three-dimensional Ricker-type discrete-time competition model. We discuss the existence and uniqueness, and find parametric conditions for local asymptotic stability of positive fixed point of this model. It is also proved that the system undergoes Neimark–Sacker (NS) and period-doubling bifurcation (PDB) at certain parametric values for positive fixed point with the help of an explicit criterion for NS and PDB. The system shows chaotic dynamics at increasing values of bifurcation parameter. To control the chaos, we apply the hybrid control methodology. Finally, numerical simulations are provided to illustrate the theoretical discussions. These results of numerical simulations show 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 model.