Dynamics of solutions of a reaction-diffusion equation with delayed inhibition

Reaction-diffusion equation with a logistic production term and a delayed inhibition term is studied. Global stability of the homogeneous in space equilibrium is proved under some conditions on the delay term. In the case where these conditions are not satisfied, this solution can become unstable resulting in the emergence of spatiotemporal pattern formation studied in numerical simulations. © 2020 American Institute of Mathematical Sciences. All rights reserved