Species migration induced by fear triggers synchrony in two-habitat system

We study the dynamics of a dual-habitat system using modified versions of the Hastings–Powell model, revealing the complex behavior within the system. In the first habitat, two predators hunt prey, with the top predator being an omnivore that hunts both the intermediate predator and the prey. In contrast, the second habitat features a solitary predator chasing prey that are protected by refugia (safe zones) and influenced by the Allee effect (a phenomenon where a prey’s growth rate decreases at low densities). In the first habitat, we incorporate the fear effect induced by the presence of both predators into the prey’s birth rate, reducing its growth. We study the system’s positivity, boundedness, dissipation, bifurcation, and extinction scenarios, alongside parameter analysis and chaos characterization. Our analysis shows that the fear of the intermediate predator causes a permanent shift in the system’s dynamics, while fear of the top predator leads to a shift from stable to chaotic dynamics. We introduce a linear migration function to couple both habitats, where species migrate from the habitat affected by fear to the one where prey growth is influenced by refugia and the Allee effect. Using singular perturbation theory and Tikhonov’s theorem, we analyze the system’s behavior as the migration rate approaches infinity. This study particularly focuses on investigating how varying migration levels across dimensions affect species synchrony between habitats. We test each possible case of the coupling dimension coefficient (CDC) to identify optimal coupling schemes for habitat sustainability. Instead of the traditional sine function, we use a cosine function to measure relative phase as a synchrony indicator. Our findings, validated through numerical simulations, suggest that ecological balance in the dual-habitat system can be achieved through single-species migration. Moreover, the presence of refugia and Allee effects supports species in attaining synchrony.