Stability of synchronized chaos in coupled dynamical systems
By Govindan Rangarajan, Mingzhou Ding. 2002
142 citations recorded by the source corpus.
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on coupling strengths which ensure the stability of synchronized chaos. Previous results in this area involving particular coupling schemes (e.g., global coupling and nearest neighbor diffusive coupling) are included as special cases of the present work.
Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e05f3ea6a70733228f1c259f8b8434e6aa207969
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In Computer Networks and Communications
In Statistical and Nonlinear Physics
Citations in the corpus
- Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models (2004, methodology): “…simplicity, assume that the coupling is symmetric, i.e. bij = bji and bij ≥ 0 (i 6= j) but not all zero, with the diffusive coupling connection [Pogromsky & Nijmeijer, 2001; Rangarajan & Ding, 2002; Wang & Chen, 2002a, 2002b; Wu & Chua, 1995]: N ∑ j=1 bij = N ∑ j=1 bji = 0 , i = 1, 2, . . . , N .”
- Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint (2003, methodology): “Remark 2: It should be noted that condition (11) appears to be similar to some results given in [19] and [ 26 ], where actually”
- Global synchronization and asymptotic stability of complex dynamical networks (2006, background): “Recently, synchronization in different small-world and scale-free dynamical network models has also been carefully studied [6]–[12].”
- Pinning a complex dynamical network to its equilibrium (2004, background): “Recall the concept of TLEs [3], [30], [ 35 ] for (17), denoted by , for each ,d efined by”