Optimal control of a population dynamics model with hysteresis

Bin Chen, Sergey A. Timoshin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)283-298
Number of pages16
JournalActa Mathematica Scientia
Issue number1
Publication statusPublished - Jan 2022
Externally publishedYes


  • 49J20
  • 49J21
  • 49J45
  • 49J53
  • biological diffusion models
  • hysteresis
  • nonconvex control constraints
  • nonconvex integrands
  • optimal control problem


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