| Volume 9, Number 1, 2019, Pages 31-44 DOI：10.11948/2019.31 |
| Bifurcations and chaos control in a discrete-time predator-prey system of Leslie type |
| Sarker Md. Sohel Rana |
| Keywords:Discrete-time predator-prey system, bifurcations, chaos, Lyapunov exponents, feedback control. |
| Abstract: |
| We investigate the dynamics of a discrete-time predator-prey system of Leslie type. We show algebraically that the system passes through a flip bifurcation and a Neimark-Sacker bifurcation in the interior of $\R^{2}_+$ using center manifold theorem and bifurcation theory. Numerical simulations are implimented not only to validate theoretical analysis but also exhibits chaotic behaviors, including phase portraits, period-11 orbits, invariant closed circle, and attracting chaotic sets. Furthermore, we compute Lyapunov exponents and fractal dimension numerically to justify the chaotic behaviors of the system. Finally, a state feedback control method is applied to stabilize the chaotic orbits at an unstable fixed point. |
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