Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations

Detalhes bibliográficos
Autor(a) principal: Almeida, Ricardo
Data de Publicação: 2022
Outros Autores: Agarwal, Ravi P., Hristova, Snezhana, O’Regan, Donal
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/33512
Resumo: A model of gene regulatory networks with generalized proportional Caputo fractional derivatives is set up, and stability properties are studied. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are discussed, and also, their application to fractional order systems and the advantage of quadratic functions are pointed out. The equilibrium of the generalized proportional Caputo fractional model and its generalized exponential stability are defined, and sufficient conditions for the generalized exponential stability and asymptotic stability of the equilibrium are obtained. As a special case, the stability of the equilibrium of the Caputo fractional model is discussed. Several examples are provided to illustrate our theoretical results and the influence of the type of fractional derivative on the stability behavior of the equilibrium.
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spelling Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equationsModel of gene regulatory networksGeneralized proportional Caputo fractional derivativesEquilibriumGeneralized exponential stabilityLyapunov functionsA model of gene regulatory networks with generalized proportional Caputo fractional derivatives is set up, and stability properties are studied. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are discussed, and also, their application to fractional order systems and the advantage of quadratic functions are pointed out. The equilibrium of the generalized proportional Caputo fractional model and its generalized exponential stability are defined, and sufficient conditions for the generalized exponential stability and asymptotic stability of the equilibrium are obtained. As a special case, the stability of the equilibrium of the Caputo fractional model is discussed. Several examples are provided to illustrate our theoretical results and the influence of the type of fractional derivative on the stability behavior of the equilibrium.MDPI2022-03-16T16:20:06Z2022-01-01T00:00:00Z2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/33512eng10.3390/e24030372Almeida, RicardoAgarwal, Ravi P.Hristova, SnezhanaO’Regan, Donalinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:04:22Zoai:ria.ua.pt:10773/33512Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:04:53.105714Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
title Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
spellingShingle Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
Almeida, Ricardo
Model of gene regulatory networks
Generalized proportional Caputo fractional derivatives
Equilibrium
Generalized exponential stability
Lyapunov functions
title_short Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
title_full Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
title_fullStr Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
title_full_unstemmed Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
title_sort Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
author Almeida, Ricardo
author_facet Almeida, Ricardo
Agarwal, Ravi P.
Hristova, Snezhana
O’Regan, Donal
author_role author
author2 Agarwal, Ravi P.
Hristova, Snezhana
O’Regan, Donal
author2_role author
author
author
dc.contributor.author.fl_str_mv Almeida, Ricardo
Agarwal, Ravi P.
Hristova, Snezhana
O’Regan, Donal
dc.subject.por.fl_str_mv Model of gene regulatory networks
Generalized proportional Caputo fractional derivatives
Equilibrium
Generalized exponential stability
Lyapunov functions
topic Model of gene regulatory networks
Generalized proportional Caputo fractional derivatives
Equilibrium
Generalized exponential stability
Lyapunov functions
description A model of gene regulatory networks with generalized proportional Caputo fractional derivatives is set up, and stability properties are studied. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are discussed, and also, their application to fractional order systems and the advantage of quadratic functions are pointed out. The equilibrium of the generalized proportional Caputo fractional model and its generalized exponential stability are defined, and sufficient conditions for the generalized exponential stability and asymptotic stability of the equilibrium are obtained. As a special case, the stability of the equilibrium of the Caputo fractional model is discussed. Several examples are provided to illustrate our theoretical results and the influence of the type of fractional derivative on the stability behavior of the equilibrium.
publishDate 2022
dc.date.none.fl_str_mv 2022-03-16T16:20:06Z
2022-01-01T00:00:00Z
2022
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/33512
url http://hdl.handle.net/10773/33512
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/e24030372
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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