Innate behavioral mechanisms and defensive traits in ecological models of predator-prey types

Phenotypic plasticity enables prey species to develop inducible defences in response to predation risk, significantly influencing predator-prey interactions. In this study, we propose a nonlinear predator-prey model in which prey exhibit inducible defense mechanisms, while predators experience mutual interference described by a Beddington-DeAngelis functional response. The analysis reveals a stabilizing effect of prey defense on system dynamics. Interestingly, predator density increases with moderate levels of interference when prey defense is weak but declines monotonically as defense strength increases. When handling time is used as a bifurcation parameter, a bistable regime emerges, highlighting the importance of initial population densities. Extending the model to a spatial setting shows that stronger defences shrink the Turing instability domain. Furthermore, incorporating predator and prey taxis exerts an additional stabilizing effect by suppressing the formation of spatial patterns. These results emphasize the critical role of inducible defences and movement strategies in shaping both temporal and spatial ecological dynamics. Altogether, the model represents a nonlinear, nonequilibrium system where pattern formation arises from the interplay between reaction kinetics, diffusion, and cross-diffusion (taxis). The results contribute to the understanding of self-organization mechanisms in interacting particle-like systems with density-dependent interactions.