Optimal control of stochastic lattice of prey-predator models

We propose a stochastic lattice model to describe the dynamics of two animal species population, one being a prey and the other a predator. The system follows a stochastic dynamics composed of three Markovain processes: the first one describes the birth of prey; the second describes the death of prey and simultaneous birth of predator, the third describes spontaneous death of predator. The master equation is used to derive the time evolution of one and two site correlations. The stability of the stationary states of one-site correlations is studied. The optimal control functions that ensure the asymptotic stability of unstable stationary states are derived. In the case of one site approximation the densities of the vacant sites, prey sites and predator sites are obtained as functions of time for the controlled model.