Global synchronization and asymptotic stability of complex dynamical networks

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 53; no. 1; pp. 28 - 33
• Main Authors: Li, Zhi, Chen, Guanrong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2006; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Asymptotic stability; Chaos; Circuits; complex network; Complex networks; Couplings; Dynamical systems; Equations; global synchronization; Large-scale systems; Lyapunov exponents; Lyapunov method; Networks; Oscillators; Stability; Sufficient conditions; Symmetric matrices; Synchronism; Synchronization
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2005.854315

Global synchronization and asymptotic stability of complex dynamical networks are investigated in this paper. Based on a reference state, a sufficient condition for global synchronization and stability is derived. Unlike other approaches where only local results were obtained, the complex network is not linearized in this paper. Instead, the sufficient condition for the global synchronization and asymptotical stability is obtained here by introducing a reference state with the Lyapunov stability theorem rather than the Lyapunov exponents, and this condition is simply given in terms of the network coupling matrix therefore is very convenient to use. Furthermore, the developed technique is applied to networks consisting of nodes with unknown but bounded nonlinear functions. A typical example of a complex network with chaotic nodes is finally used to verify the theoretical results and the effectiveness of the proposed synchronization scheme