Optimal control of non-homogeneous prey–predator models during infinite and finite time intervals

We propose a lattice to describe dynamics of two animal species population, one being a prey and the other a predator. The problem of controlling steady-states of non-homogeneous prey–predator model during finite and infinite time intervals is studied using Lyapunov Bellman technique. The optimal control law is derived from the conditions that ensure the asymptotic stabilization of the steady-states of this model using Bellman's equation. The densities of both prey and predator populations are obtained as functions of time. Graphical and numerical example studies of the obtained results are presented.