Optimal control of a population dynamics model with hysteresis
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.
Cite
@article{arxiv.2104.09219,
title = {Optimal control of a population dynamics model with hysteresis},
author = {Sergey A. Timoshin and Chen Bin},
journal= {arXiv preprint arXiv:2104.09219},
year = {2021}
}