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arXiv · 2104.09219

Optimal control of a population dynamics model with hysteresis

Sergey A. Timoshin·Chen Bin
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Abstract

This paper addresses a nonlinear partial differential control system arising in population dynamics. The system consist of three diffusion equations describing the evolutions of three biological species: prey, predator, and food for the prey or vegetation. The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process. We study the problem of minimization of a given integral cost functional over solutions of the above system. The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable. Some relaxation-type results for the minimization problem are obtained and the existence of a nearly optimal solution is established.

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Sergey A. Timoshin, Chen Bin. 2021-04-19. Optimal control of a population dynamics model with hysteresis. https://arxiv.org/abs/2104.09219

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