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Optimal Control of a Population Dynamics Model with Hysteresis by Timoshin, Sergey A.; Bin, Chen is a scholarly article available to read on EtoBox.

What is Optimal Control of a Population Dynamics Model with Hysteresis about?

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.

Author

Timoshin, Sergey A.; Bin, Chen

Published

2021

Language

EN