Hopf bifurcation and chaos in a Leslie-Gower prey-predator model with discrete delays. (English) Zbl 1461.92099
This article explores Leslie’s multiple deferred prey model. In this paper, the presence of a Hopf bifurcation for various combinations of discrete delays τ1 and τ2 on the dynamics of the model is established. The Hopf bifurcation is responsible for switching a stable system to an instable one with respect to delays. The model demonstrates a wide range of complex dynamics from stability to chaos, including quasiperiodic solutions. The properties of periodic solutions with respect to τ1 are determined. Global stability for a system with and without latency has been established under certain conditions. It is shown that bifurcational periodic solutions are supercritical, stable, and grow with time. To confirm the theoretical conclusions of the analysis, extensive numerical simulations were carried out to illustrate the complex dynamics of the system, namely, periodicity, quasiperiodicity, and chaos. This study can help draw conclusions about population dynamics with different lag times.
Reviewer: Fatima T. Adylova (Tashkent)
MSC:
| 92D25 | Population dynamics (general) |
| 34K23 | Complex (chaotic) behavior of solutions to functional-differential equations |
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