Dynamics of prey-predator interactions embedded with global warming and prosocial behavioral frameworks

Abstract This work develops a five-dimensional eco-epidemiological model that connects evolutionary game theory, warming-related environmental stress feedbacks, predator population growth, and susceptible-infected prey dynamics. The system accounts for temperature-sensitive predator physiology, wind-modulated Holling Type-II predation, fear-induced reductions in prey reproduction, and adaptive behavioral strategies—a departure from standard formulations that assume static interactions. This behavioral adaptation is driven by a replicator equation that directly connects strategy adoption to decreased disease transmission. The predator intrinsic growth rate ( $$r_2$$ ) and the predation pressure on infected prey ( $$\alpha _I$$ ) are identified as the main organizing centers of high-codimension dynamics via two-parameter bifurcation numerical continuation. A network of Generalized Hopf (Bautin), Bogdanov-Takens, and Chenciner bifurcations is anchored by a Hopf-Hopf (HH) bifurcation in the parameter space. Arnold tongues and quasiperiodic tori with strong resonances (1:2, 1:3, 1:4) are produced by this topological structure. We prove that this topological complexity is strictly bounded by the predator productivity limit by comparing these results with the demographic ( $$r_1$$ ), operational ( h ), and thermal stress ( $$\xi _2$$ ) limits. As a result, $$r_2$$ serves as the primary control parameter that drives the system from stable limit cycles to chaos. The system settles into a strange attractor with a positive maximal Lyapunov exponent after three Generalized Period-Doubling (GPD) bifurcations, imposing a stringent predictability horizon on disease outbreaks. Ultimately, these findings demonstrate that the combination of predator-driven disease suppression, behavioral evolution, and climate feedbacks produces intrinsic unpredictability. Such dynamics seriously threaten the sustainability of conventional threshold-based ecological management in warming environments.