Global solvability of prey-predator models with indirect predator-taxis

Abstract

This paper analyzes prey-predator models with indirect predator-taxis in such a way that chemical secreted by the predator triggers the repellent behavior of prey against the predator. Under the assumption of quadratic decay of predator, we prove the global existence and uniform boundedness of classical solutions up to two spatial dimensions. Moreover, via the linear stability analysis, we show that large chemosensitivity gives rise to the occurrence of pattern formations. We also obtain the global stability results for the nontrivial constant steady states by establishing proper Lyapunov functionals.