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Optimal control of non-homogeneous prey–predator models during infinite and finite time intervals. (English) Zbl 1026.92044

Summary: We propose a lattice to describe dynamics of two animal species populations, 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 techniques. 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.

MSC:

92D40 Ecology
92D25 Population dynamics (general)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
93E20 Optimal stochastic control
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