On the formulation and solution of the isochronal synchronization stability problem in delay-coupled complex networks | Zendy

J.M.V. Grzybowski | Zendy; Elbert E. N. Macau | Zendy; Takashi Yoneyama | Zendy

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On the formulation and solution of the isochronal synchronization stability problem in delay-coupled complex networks

Author(s) -

J.M.V. Grzybowski,

Elbert E. N. Macau,

Takashi Yoneyama

Publication year - 2012

Publication title -

chaos an interdisciplinary journal of nonlinear science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.971

H-Index - 113

eISSN - 1089-7682

pISSN - 1054-1500

DOI - 10.1063/1.4753921

Subject(s) - synchronization (alternating current) , transformation (genetics) , dimension (graph theory) , state vector , state (computer science) , control theory (sociology) , stability (learning theory) , mathematics , lyapunov stability , basis (linear algebra) , computer science , topology (electrical circuits) , algorithm , pure mathematics , artificial intelligence , physics , biochemistry , chemistry , geometry , control (management) , classical mechanics , combinatorics , machine learning , gene

We present a new framework to the formulation of the problem of isochronal synchronization for networks of delay-coupled oscillators. Using a linear transformation to change coordinates of the network state vector, this method allows straightforward definition of the error system, which is a critical step in the formulation of the synchronization problem. The synchronization problem is then solved on the basis of Lyapunov-Krasovskii theorem. Following this approach, we show how the error system can be defined such that its dimension can be the same as (or smaller than) that of the network state vector.

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