Fear-mediated invasion dynamics in a two-predator–one-prey model

Biological invasions frequently restructure native food webs through a combination of direct consumption and non-consumptive risk effects. However, many theoretical invasion frameworks do not explicitly track predator-specific prey responses to native versus novel predators. This study examines a deterministic three-species model describing the invasion of an exotic generalist predator into a resident community comprising a shared prey and a native specialist predator. The model integrates a predator-specific fear kernel alongside saturating functional responses and direct competitive interference. We derive analytical invasion thresholds for the feasible boundary equilibria and use numerical continuation to show that the qualitative outcome depends on which predator elicits the stronger prey response. Strong fear of the native predator creates a bistable regime where invasion success depends on initial population densities rather than invasion from rarity alone. In contrast, strong prey fear of the exotic predator drives the system through a supercritical Hopf bifurcation, generating sustained oscillations of growing amplitude that ultimately force native predator exclusion. Two-parameter continuation further shows that the oscillatory and fold instabilities in the exotic fear regime share a common codimension-two origin, establishing that these routes to native predator exclusion are structurally linked rather than independent. These results show that the direction of prey fear asymmetry determines which route to community instability is taken, and that non-consumptive effects alone are sufficient to generate qualitatively distinct invasion outcomes in a multi-predator community.