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.
Bin CHEN
,
Sergey A. TIMOSHIN
. OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS[J]. Acta mathematica scientia, Series B, 2022
, 42(1)
: 283
-298
.
DOI: 10.1007/s10473-022-0116-x
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