Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense

Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense

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In this paper, we investigate the dynamics of a discrete-time gewehr 91 predator-prey system involving group defense.The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically.It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory.

Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set.The Lyapunov exponents jerome brown jersey are numerically computed to characterize the complexity of the dynamical behaviors.