Bifurcations and chaos control in a discrete-time predator-prey system of Leslie type |
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Authors: | Sarker Md Sohel Rana |
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Institution: | Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh |
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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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Keywords: | Discrete-time predator-prey system bifurcations chaos Lyapunov exponents feedback control |
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