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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
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
DOI: 10.3390/e24030372
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