Chaos and Bifurcation of Fractional Discrete-Time Population Model

Abstract

A Leslie population model is an interesting mathematical discrete-time system because of its significant and wide applications in biology and ecology. In this paper, we extensively studied a fractional Leslie population model in the fractional μ-Caputo sense. For the different fractional order value and system parameters, the dynamics of the fractional population model are studied. It is verified that the new fractional population model undergoes doubling route to chaos and Neimark-Sacker bifurcation. Moreover, The dynamic of this model is experimentally investigated via bifurcation diagrams, phase portraits, largest Lyapunov exponent. Furthermore, the chaotic dynamic of the proposed population model is confirmed using a 0-1 test method. Simulation results reveal that chaos can be observed in such fractional model and its dynamic behavior depends on the fractional order value.