Effect of immigration in a predator-prey system: Stability, bifurcation and chaos
Date
02/06/2022Metadata
Show full item recordCitation
Kangalgil, F., & Isșık, S. (2022). Effect of immigration in a predator-prey system: Stability, bifurcation and chaos. AIMS Mathematics, 7(8), 14354-14375.Abstract
In the present manuscript, a discrete-time predator-prey system with prey immigration is
considered. The existence of the possible fixed points of the system and topological classification of
coexistence fixed point are analyzed. Moreover, the existence and the direction for both Neimark-
Sacker bifurcation and flip bifurcation are investigated by applying bifurcation theory. In order to
control chaos due to the emergence of the Neimark-Sacker bifurcation, an OGY feedback control
strategy is implemented. Furthermore, some numerical simulations, including bifurcation diagrams,
phase portraits and maximum Lyapunov exponents of the system, are given to support the accuracy of
the analytical finding. The computation of the maximum Lyapunov exponents confirms the presence
of chaotic behavior in the system.