Bifurcation and chaos analysis for a discrete ecological developmental systems.

This work concentrates on the dynamic analysis including bifurcation and chaos of a discrete ecological developmental systems. Specifically, it is a prey-predator-scavenger (PPS) system, which is derived by Euler discretization method. By choosing the step size as a bifurcation parameter, we determine the set consists of all system's parameters, in which the system can undergo flip bifurcation (FB) and Neimark-Sacker bifurcation (NSB). The theoretical results are verified by some numerical simulations. It is shown that the discrete systems exhibit more interesting behaviors, including the chaotic sets, quasi-periodic orbits, and the cascade of period-doubling bifurcation in orbits of periods 2, 4, 8, 16. Finally, corresponding to the two bifurcation behaviors discussed, the maximum Lyapunov exponent is numerically calculated, which further verifies the rich dynamic characteristics of the discrete system.