Uniform Boundedness of Solutions for a Predator-Prey System with Diffusion and Chemotaxis

This paper deals with a nonlinear system of reaction-diffusion partial differential equations modelling the evolution of a prey-predator biological system with chemotaxis. The system is constituted by three coupled equations: a fully parabolic chemotaxis system describing the behavior of the active predators and preys and an ordinary equation, describing the dynamics of the dormant predators, coupled to it. Chemotaxis in this context affects the active predators so that they move towards the regions where the density of resting eggs (dormant predators) is higher. Under suitable assumptions on the initial data and the coefficients of the system, the global-in-time existence of classical solutions is proved in any space dimension. Besides, numerical simulations are performed to illustrate the behavior of the solutions of the system. The theoretical and numerical findings show that the model considered here can provide very interesting and complex dynamics.