Stability analysis for coupled systems of fractional differential equations on networks

ABSTRACT

This paper considers the stability problem for some coupled systems of fractional differential equations on networks (CSFDENs). We provide a systematic method for constructing a Lyapunov function for CSFDENs by using graph theory and the Lyapunov method. Consequently, some sufficient conditions for stability, uniform stability and uniform asymptotic stability of CSFDENs are obtained. Finally, an example and some numerical simulations are presented to verify the effectiveness of the theoretical results.

KEYWORDS:

• stability
• coupled systems on networks
• fractional differential equations
• graph theory
• Lyapunov function

2010 AMS SUBJECT CLASSIFICATIONS:

• 34A08
• 34D20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (Grant Nos. 11371287,11361059,11501498), the International Science and Technology Cooperation Program of China (Grant No. 2010DFA14700), Xinjiang Introduction Plan Project of High Level Talents, the Natural Science Foundation of Xinjiang (Grant No. 2012211B07), and the Scientific Research Programmes of Colleges in Xinjiang (XJEDU2013I03).