Relaxation in population dynamics models with hysteresis

Sergey A. Timoshin; Toyohiko Aiki

doi:10.1137/19M1279551

Relaxation in population dynamics models with hysteresis

Sergey A. Timoshin^*, Toyohiko Aiki

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

The present paper is concerned with a nonlinear partial differential control system subject to a state-dependent and nonconvex control constraint. This system models the dynamics of populations in the vegetation-prey-predator framework and takes account of diffusive and hysteresis effects appearing in the process. We prove the existence of solutions to our system and show that they are close in a suitable sense to solutions of the system with the convexified control constraint.

Original language	English
Pages (from-to)	693-708
Number of pages	16
Journal	SIAM Journal on Control and Optimization
Volume	59
Issue number	1
DOIs	https://doi.org/10.1137/19M1279551
Publication status	Published - 2021
Externally published	Yes

Keywords

Biological diffusion models
Evolution control systems
Hysteresis
Relaxation
State-dependent constraints

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10.1137/19M1279551

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abstract = "The present paper is concerned with a nonlinear partial differential control system subject to a state-dependent and nonconvex control constraint. This system models the dynamics of populations in the vegetation-prey-predator framework and takes account of diffusive and hysteresis effects appearing in the process. We prove the existence of solutions to our system and show that they are close in a suitable sense to solutions of the system with the convexified control constraint.",

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AU - Timoshin, Sergey A.

AU - Aiki, Toyohiko

PY - 2021

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N2 - The present paper is concerned with a nonlinear partial differential control system subject to a state-dependent and nonconvex control constraint. This system models the dynamics of populations in the vegetation-prey-predator framework and takes account of diffusive and hysteresis effects appearing in the process. We prove the existence of solutions to our system and show that they are close in a suitable sense to solutions of the system with the convexified control constraint.

AB - The present paper is concerned with a nonlinear partial differential control system subject to a state-dependent and nonconvex control constraint. This system models the dynamics of populations in the vegetation-prey-predator framework and takes account of diffusive and hysteresis effects appearing in the process. We prove the existence of solutions to our system and show that they are close in a suitable sense to solutions of the system with the convexified control constraint.

KW - Biological diffusion models

KW - Evolution control systems

KW - Hysteresis

KW - Relaxation

KW - State-dependent constraints

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U2 - 10.1137/19M1279551

DO - 10.1137/19M1279551

M3 - Article

AN - SCOPUS:85101880645

SN - 0363-0129

VL - 59

SP - 693

EP - 708

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 1

ER -

Relaxation in population dynamics models with hysteresis

Abstract

Keywords

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