Optimization of a Prey–Predator Model with Hysteresis and Convection

Chen Bin; Xiao Yu Liang; Emil Minchev; Sergey A. Timoshin

doi:10.1007/s10957-023-02225-0

Optimization of a Prey–Predator Model with Hysteresis and Convection

Chen Bin, Xiao Yu Liang, Emil Minchev, Sergey A. Timoshin^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	347-371
Number of pages	25
Journal	Journal of Optimization Theory and Applications
Volume	198
Issue number	1
DOIs	https://doi.org/10.1007/s10957-023-02225-0
Publication status	Published - Jul 2023
Externally published	Yes

Keywords

Convection
Hysteresis
Nonconvex optimal control problems
Prey–predator diffusion models

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10.1007/s10957-023-02225-0

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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 = "Convection, Hysteresis, Nonconvex optimal control problems, Prey–predator diffusion models",

author = "Chen Bin and Liang, {Xiao Yu} and Emil Minchev and Timoshin, {Sergey A.}",

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PY - 2023/7

Y1 - 2023/7

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AB - 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.

KW - Convection

KW - Hysteresis

KW - Nonconvex optimal control problems

KW - Prey–predator diffusion models

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IS - 1

ER -

Optimization of a Prey–Predator Model with Hysteresis and Convection

Abstract

Keywords

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