Abstract
In this paper, the stability problem of a new coupled model constructed by two fractional-order differential equations for every vertex is studied. The coupled relationship is hybrid. By using the method of constructing Lyapunov functions based on graph-theoretical approach for coupled systems, sufficient conditions that the coexistence equilibrium of the coupling model is globally Mittag–Leffler stable in R^{2n} are derived. An example is given to illustrate the main results.
Highlights
The global-stability problem of equilibria has been investigated for coupled systems of differential equations on networks for many years [1,2,3,4,5,6]
By using the method of constructing Lyapunov functions based on graph-theoretical approach for coupled systems, sufficient conditions that the coexistence equilibrium of the coupling model (2) is globally Mittag–Leffler stable in R2n are derived
The new coupled model constructed by two fractional-order differential equations for every vertex is studied
Summary
The global-stability problem of equilibria has been investigated for coupled systems of differential equations on networks for many years [1,2,3,4,5,6]. There exist many results about stability of coupled systems on networks (CSNs), most efforts have been devoted to CSNs whose nodes are constructed by integer-order differential equations. It is more valuable and practical to investigate a coupled system of fractional-order differential equations on the network.
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