Chaotic bifurcation dynamics in predator–prey interactions with logistic growth and Holling type-II response

Abstract

This manuscript focuses on the dynamical properties of a discrete-time predator–prey model with a functional response of Holling type-II. Utilizing linear stability analysis, we determine the conditions required to ensure the existence and stability of the system’s equilibrium points. Additionally, we utilize the center manifold theory along with bifurcation analysis and investigate the occurrence of period-doubling (PD) and Neimark–Sacker (NS) bifurcations. In order to verify our theoretical findings and uncover new complex patterns within the system, we conduct extensive numerical simulations. These simulations not only validate our theoretical predictions but also reveal intricate dynamics characterized by bifurcation diagrams, phase portraits especially before and after bifurcation and maximal Lyapunov exponent (MLE) plots. The computation of MLE is particularly significant, as it allows us to distinguish between chaotic and regular behaviors within the system. As the system transitions from bifurcation to chaos, we observe a variety of patterns such as spiral structure, irregular orbits, scattered points and chaotic bursts. Our research makes a significant contribution to the broader field of ecological modeling by providing a deeper understanding of the complex behaviors in natural predator–prey interactions.

Keywords

• Discrete population dynamics
• Stability analysis
• Center manifold theory
• Bifurcation
• Simulation-based analysis