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Pinning chaotic synchronization in complex networks on maximum eigenvalue of low order matrix. (Chinese. English summary) Zbl 1265.93137

Summary: We find the decreasing law of maximum eigenvalue of the principal sub-matrix for coupling matrix, propose a method of calculating quickly pinning nodes in complex networks, and reveal the relation between the pinning strategy and the number pinning nodes. Numerical simulations show the trends of evolution under the conditions of three pinning strategies in a scale-free network and a small world, and the effectiveness of the pinning synchronization by selecting pinning nodes randomly in a scale-free network.

MSC:

93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
91D30 Social networks; opinion dynamics
05C82 Small world graphs, complex networks (graph-theoretic aspects)