Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
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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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 |
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instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137704243363840 |