TY - JOUR
T1 - Control of biological models with hysteresis
AU - Timoshin, Sergey A.
AU - Aiki, Toyohiko
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/6
Y1 - 2019/6
N2 - This article presents a control problem in population dynamics when diffusive and hysteretic effects in the evolution of population are taken into account. Namely, we consider a diffusive prey–predator model, in a bounded domain, with a parameter corresponding to the quantity of food for the preys. In the model, the evolution of the food density is described by a hysteresis operator of the generalized play type whose inputs are the densities of preys/predators. Roughly speaking, the rate of change of the food density depends not only on the present state of preys/predators, but also on their immediately preceding density history. Our main concern is to extend the previous research of this model by controlling the food supply and to study the well-posedness of the corresponding dynamical control problem.
AB - This article presents a control problem in population dynamics when diffusive and hysteretic effects in the evolution of population are taken into account. Namely, we consider a diffusive prey–predator model, in a bounded domain, with a parameter corresponding to the quantity of food for the preys. In the model, the evolution of the food density is described by a hysteresis operator of the generalized play type whose inputs are the densities of preys/predators. Roughly speaking, the rate of change of the food density depends not only on the present state of preys/predators, but also on their immediately preceding density history. Our main concern is to extend the previous research of this model by controlling the food supply and to study the well-posedness of the corresponding dynamical control problem.
KW - Biological diffusion models
KW - Control systems
KW - Hysteresis
UR - http://www.scopus.com/inward/record.url?scp=85065535327&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2019.04.003
DO - 10.1016/j.sysconle.2019.04.003
M3 - Article
AN - SCOPUS:85065535327
SN - 0167-6911
VL - 128
SP - 41
EP - 45
JO - Systems and Control Letters
JF - Systems and Control Letters
ER -