Repulsive chemotaxis and predator evasion in predator–prey models with diffusion and prey-taxis

The role of predator evasion mediated by chemical signaling is studied in a diffusive prey–predator model when prey-taxis taken into account (model A) or not B) with taxis strength coefficients [Formula: see text] and text], respectively. In the kinetic part models, it assumed that rate prey consumption includes functional responses Holling, Beddington–DeAngelis Crowley–Martin. Existence global-in-time classical solutions to A proved space dimension while B for any text]. Crowley–Martin response combined bounded signal production precludes blow-up solution Local global stability constant coexistence steady state which stable corresponding ordinary differential equation (ODE) purely are along mechanism Hopf bifurcation exceeds some critical value. A, shown may destabilize provided big enough. Numerical simulation depicts emergence complex space-time patterns both models indicates existence finite time