Optimization of a Prey–Predator Model with Hysteresis and Convection

Chen Bin, Xiao Yu Liang, Emil Minchev and Sergey A. Timoshin ()
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Chen Bin: Huaqiao University
Xiao Yu Liang: Huaqiao University
Emil Minchev: Hikari Ltd
Sergey A. Timoshin: Huaqiao University

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 1, No 13, 347-371

Abstract: Abstract A nonconvex optimal control problem for a partial differential system is proposed and analyzed. Our nonlinear control system can be interpreted in the population dynamics framework when, along with diffusional, hysteretic and migratory effects in the evolution of biological species are accounted for. We prove the existence of a nearly optimal solution to the optimization problem through relaxation-type properties; we establish for the underlying minimizing cost functional and control system.

Keywords: Hysteresis; Convection; Prey–predator diffusion models; Nonconvex optimal control problems; 49J20; 49J21; 49J45; 49J53 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02225-0

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