Discrete-time systems with random switches: From systems stability to networks synchronization
- School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433 (China)
- Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Hong Kong (China)
In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developed approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.
- OSTI ID:
- 22596862
- Journal Information:
- Chaos (Woodbury, N. Y.), Vol. 26, Issue 3; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
- Country of Publication:
- United States
- Language:
- English
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