Abstract
The present study focuses on the dynamical aspects of a discrete-time Leslie-Gower predator-prey model accompanied by a Holling type III functional response. Discretization is conducted by applying a piecewise constant argument method of differential equations. Moreover, boundedness, existence, uniqueness, and a local stability analysis of biologically feasible equilibria were investigated. By implementing the center manifold theorem and bifurcation theory, our study reveals that the given system undergoes period-doubling and Neimark-Sacker bifurcation around the interior equilibrium point. By contrast, chaotic attractors ensure chaos. To avoid these unpredictable situations, we establish a feedback-control strategy to control the chaos created under the influence of bifurcation. The fractal dimensions of the proposed model are calculated. The maximum Lyapunov exponents and phase portraits are depicted to further confirm the complexity and chaotic behavior. Finally, numerical simulations are presented to confirm the theoretical and analytical findings.
Highlights
Various fundamental aspects of the nonlinear dynamics of predatorprey population models related to continuous dynamical systems have been studied, the characteristics of discrete dynamical systems remain comparatively unknown
We examined the qualitative and dynamical analyses of a discrete-time predator-prey model
It was proved that the population sustains both period-doubling bifurcation and Neimark-Sacker bifurcation near the interior equilibrium
Summary
([32]) Let f : I → I be a map and x ∗ be a fixed point of f , where I is an interval in the set of real numbers R. ([32]) A fixed point x ∗ of a map f is said to be hyperbolic if | f 0 ( x ∗ )| = 1. ([32]) Let x ∗ be a hyperbolic fixed point of a map f , where f is continuously differentiable at x ∗. The following statements hold true: If | f 0 ( x ∗ )| < 1, x ∗ is asymptotically stable. If | f 0 ( x ∗ )| > 1, x ∗ is unstable
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
