Indirect taxis drives spatio-temporal patterns in an extended Schoener’s intraguild predator–prey model

In Schoener’s model of intraguild-predation a prey-predator interaction is mixed with the competition of the prey and the predator for food resource supplied to a system with a constant rate. In this work the model is extended to examine the impact of indirect prey taxis which counts for the movement of predator towards the odor released by prey rather than directly towards gradient of prey density (prey taxis) and indirect predator taxis which refers to prey movement opposite to the gradient of a chemical released by predator. The constant coexistence steady state in the model was shown earlier to be globally stable when Schoener’s O.D.E. model is generalized to reaction–diffusion or even prey taxis system. Existence of global-in-time solutions to Schoener’s model with indirect prey taxis is proved for any space dimension while for the case of indirect predator taxis only in 1D. This study reveals that sufficiently large value of taxis sensitivity parameter disturbs the stability of the coexistence steady state giving rise to pattern formation governed by the Hopf bifurcation. Numerical simulations illustrate emergence of taxis driven spatio-temporal periodic patterns.