Abstract
Based on the graph theory and stability theory of dynamical system, this paper studies the stability of the trivial solution of a coupled fractional-order system. Some sufficient conditions are obtained to guarantee the global stability of the trivial solution. Finally, a comparison between fractional-order system and integer-order system ends the paper.
Highlights
Due to the great significance in applied science, the neural networks have attracted many scholars’ attention.There are a large amount of scientific research results on the stability and synchronization of both integer-order and fractional-order differential equations
We apply the graph theory and stability theory of dynamical system to study the stability of a coupled fractional-order system
This method can be extended to the other complex networks or multi-layer networks
Summary
Due to the great significance in applied science (e.g., signal and image processing, artificial intelligence, pattern classification), the neural networks have attracted many scholars’ attention. It is worthwhile to mention that the fractional-order impulsive differential equations were studied recently (see e.g., [29,30,31,32,33,34,35,36]). Stamov and Stamova [31,32,33,34] studied the almost periodicity of the fractional-order impulsive differential equations. This is not valid for the fractional derivative (see [47]) This difference results in great difficulties to deal with the impulses at moment tk. ≤ −ω ( x ) < 0 implies dt = f ( x, t ), the first derivative dt the asymptotically stability in the sense of Lyapunov This classical Lyapunov stability result is not valid for fractional-order system.
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