Complexity analysis with chaos control: A discretized ratio-dependent Holling-Tanner predator-prey model with Fear effect in prey population.

This study explores a novel two-dimensional discrete-time ratio-dependent Holling-Tanner predator-prey model, incorporating the impact of the Fear effect on the prey population. The study focuses on identifying stationary points and analyzing bifurcations around the positive fixed point, with an emphasis on their biological significance. Our examination of bifurcations at the interior fixed point uncovers a variety of generic bifurcations, including one-parameter bifurcations, period-doubling, and Neimark-Sacker bifurcations. To further understand NS bifurcation, we establish non-degeneracy condition. The system's bifurcating and fluctuating behavior is managed using Ott-Grebogi-Yorke (OGY) control technique. From an ecological perspective, these findings underscore the substantial role of the Fear effect in shaping predator-prey dynamics. The research is extended to a networked context, where interconnected prey-predator populations demonstrate the influence of coupling strength and network structure on the system's dynamics. The theoretical results are validated through numerical simulations, which encompass local dynamical classifications, calculations of maximum Lyapunov exponents, phase portrait analyses, and bifurcation diagrams.