Anticipating critical transitions in fear-mediated mutualistic ecological system: Effects of stochasticity and early warning signals.

Predators rarely forage with fixed efficiency; they cooperate, adjust their search effort to prey availability, and impose non-consumptive effects such as fear, while prey often respond through mutualistic associations with non-prey partners. Yet how these adaptive feedbacks collectively shape ecosystem resilience, critical transitions, and collapse in mutualistic communities remains unresolved within a unified theoretical framework. To address this gap, we develop a community-level mathematical model integrating prey-non-prey mutualism, cooperative hunting, prey-dependent predator search efficiency, and fear-mediated reproductive suppression, and investigate how these interacting mechanisms influence ecological stability under environmental variability. Our results reveal that cooperative hunting fundamentally reorganizes the ecosystem's tipping structure. Increasing cooperation drives catastrophic regime shifts through saddle-node bifurcations, promotes oscillatory coexistence, and generates homoclinic transitions absent from earlier mutualistic predator-prey models. Mutualistic support initially enhances resilience and species persistence but, beyond a critical threshold, induces tri-stable dynamics consistent with the paradox of enrichment. Contrary to the conventional view of fear as solely detrimental, moderate fear stabilizes coexistence, whereas its interaction with strong predator cooperation triggers abrupt transitions between alternative ecological states. Furthermore, two-parameter bifurcation analysis uncovers a remarkably rich dynamical landscape containing Bogdanov-Takens, generalized Hopf, cusp, and homoclinic structures, exposing multiple pathways to ecosystem collapse and recovery that remained hidden in previous studies lacking adaptive predator behavior. Under environmental stochasticity, noise-induced switching emerges well before deterministic tipping thresholds are reached, while increasing standard deviation and lag-1 autocorrelation provide reliable early-warning signals of impending collapse. Together, these findings identify adaptive predator behavior as a key determinant of resilience, tipping dynamics, and collapse predictability in mutualistic ecosystems facing environmental change.