Behavioural Versus Physiological Fear Responses in a Pursuit-Evasion Predator–Prey Model with Constant Predator Abundance

We formulate and study a predator–prey model with pursuit-evasion spatial behaviour, incorporating the fear effect in a sexually-reproducing prey population. The pursuit-evasion movements are described as indirect taxis: populations respond to diffusively dispersed and decaying kairomonal cues of their antagonists. The prey-emitted kairomone attracts predators, while the predator-emitted kairomone repels prey and locally reduces prey reproduction rate, mimicking a physiological fear response. To isolate the net effect of predator’s prey-taxis, we assume predator birth/death rates are negligible, implying a constant predator abundance. Linear stability analysis yields a condition for taxis-driven oscillatory instability of the homogeneous steady state. Numerical simulations reveal spatially heterogeneous dynamics, coexistence of periodic travelling waves, and transitions to spatiotemporal chaos. The results highlight interrelations between fear responses, spatial movements, spatiotemporal heterogeneity, and viability of the trophic system.