Controllability and stabilization of a nonlinear hierarchical age-structured competing system
This article concerns the approximate controllability of a biological system, which is composed of two hierarchical age-structured competing species. Basing on a controllability result of linear system, we prove that the nonlinear system is approximately controllable by means of a fixed point the...
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Texas State University
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doaj-20cca31828d74cfa8c0ab7c6579837b92020-11-25T03:24:42ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912020-06-01202058,116Controllability and stabilization of a nonlinear hierarchical age-structured competing systemZe-Rong He0Nan Zhou1 Hangzhou Dianzi Univ., Hangzhou, China Hangzhou Dianzi Univ., Hangzhou, China This article concerns the approximate controllability of a biological system, which is composed of two hierarchical age-structured competing species. Basing on a controllability result of linear system, we prove that the nonlinear system is approximately controllable by means of a fixed point theorem for multi-valued mappings. To fix a suitable control policy, we deal with an optimal control problem and established the existence of the unique optimal strategy. In addition, the stabilization problem of the system is also considered.http://ejde.math.txstate.edu/Volumes/2020/58/abstr.htmlhierarchy of agepopulation systemcompetitioncontrollabilityfan-glicksberg fixed points |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ze-Rong He Nan Zhou |
spellingShingle |
Ze-Rong He Nan Zhou Controllability and stabilization of a nonlinear hierarchical age-structured competing system Electronic Journal of Differential Equations hierarchy of age population system competition controllability fan-glicksberg fixed points |
author_facet |
Ze-Rong He Nan Zhou |
author_sort |
Ze-Rong He |
title |
Controllability and stabilization of a nonlinear hierarchical age-structured competing system |
title_short |
Controllability and stabilization of a nonlinear hierarchical age-structured competing system |
title_full |
Controllability and stabilization of a nonlinear hierarchical age-structured competing system |
title_fullStr |
Controllability and stabilization of a nonlinear hierarchical age-structured competing system |
title_full_unstemmed |
Controllability and stabilization of a nonlinear hierarchical age-structured competing system |
title_sort |
controllability and stabilization of a nonlinear hierarchical age-structured competing system |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2020-06-01 |
description |
This article concerns the approximate controllability of a biological system,
which is composed of two hierarchical age-structured competing species.
Basing on a controllability result of linear system, we prove that the nonlinear
system is approximately controllable by means of a fixed point theorem for
multi-valued mappings. To fix a suitable control policy, we deal with an
optimal control problem and established the existence of the unique optimal strategy.
In addition, the stabilization problem of the system is also considered. |
topic |
hierarchy of age population system competition controllability fan-glicksberg fixed points |
url |
http://ejde.math.txstate.edu/Volumes/2020/58/abstr.html |
work_keys_str_mv |
AT zeronghe controllabilityandstabilizationofanonlinearhierarchicalagestructuredcompetingsystem AT nanzhou controllabilityandstabilizationofanonlinearhierarchicalagestructuredcompetingsystem |
_version_ |
1724600463622406144 |