Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/33512
Title: | Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations |
Author: | Almeida, Ricardo Agarwal, Ravi P. Hristova, Snezhana O’Regan, Donal |
Keywords: | Model of gene regulatory networks Generalized proportional Caputo fractional derivatives Equilibrium Generalized exponential stability Lyapunov functions |
Issue Date: | 2022 |
Publisher: | MDPI |
Abstract: | 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. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/33512 |
DOI: | 10.3390/e24030372 |
Publisher Version: | https://www.mdpi.com/1099-4300/24/3/372 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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[2022] Stability of Gene Regulatory Networks Modeled by Generalized Proportional Caputo Fractional Differential Equations.pdf | 378.2 kB | Adobe PDF | View/Open |
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