Complex dynamic transformations and strange attractors in a tri-trophic predator-prey system

Understanding predator-prey interactions is a fundamental issue in ecology, and the complex dynamics they induce are highly significant for maintaining community stability and self-organising biodiversity. Here, we investigate complex dynamical behaviors and bifurcation structures in a tri-trophic food web comprising a basal prey, an intermediate predator, and an omnivorous top predator. By combining Jacobian analysis with Hopf bifurcation theory, we derive explicit stability conditions and identify thresholds for oscillatory onset at the coexistence equilibrium. Further, we employ Shilnikov's theorem to establish criteria for the emergence of homoclinic orbit. Numerical simulations uncover a rich repertoire of dynamics, including stable limit cycles, Shilnikov homoclinic attractors, strange attractors, period-doubling cascades (with period-2 and 3 windows), chaotic bursts, and crisis-induced intermittency. These regimes are highly sensitive to the omnivore's foraging strategy: minor parameter shifts can destabilize oscillations or precipitate full system collapse. Our results highlight how omnivory and interaction structure critically modulate ecosystem complexity and resilience, offering new insights into the mechanisms that govern stability in multitrophic systems.