Codimension-one bifurcations, 0 − 1 chaos test and local behavior at fixed points of a discrete ratio-dependent predator-prey model with linear harvesting - Muhammad Rameez Raja; Abdul Qadeer Khan; J.G. AL-Juaid; Md. Rifat Hasan (Ain Shams Engineering Journal)
In this paper, we investigate codimension-one bifurcations, the 0-1 chaos test, and the local behavior at fixed points of a discrete ratio-dependent predator-prey model with linear harvesting. We begin by identifying the existence of boundary and interior fixed points under specific parametric conditions, and analyze their local stability using the linear stability theory. To understand how qualitative changes in the model's dynamics occur, we conduct a detailed codimension-one bifurcation analysis, particularly focusing on Neimark-Sacker and flip bifurcations by the bifurcation theory and center manifold theorem. The occurrence of chaotic behavior near these bifurcations is further explored using OGY and hybrid control strategies. A significant part of this study involves applying the 0-1 chaos test which is an efficient numerical algorithm designed to differentiate between regular (quasi-periodic or periodic) and chaotic dynamics based on the asymptotic growth of a translation variable derived from the model's time series. The test yields a value close to 0 for regular dynamics, and near 1 for chaotic behavior, providing a simple binary indicator of chaos. We also interpreted theoretical results biologically. Finally, theoretical results are validated and illustrated through extensive numerical simulations.