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**Adaptive pinning synchronization of complex networks with stochastic perturbations.**
*(English)*
Zbl 1198.34090

Summary: The adaptive pinning synchronization is investigated for complex networks with nondelayed and delayed couplings and vector-form stochastic perturbations. Two kinds of adaptive pinning controllers are designed. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are developed to guarantee the synchronization of the proposed complex networks even if partial states of the nodes are coupled. Furthermore, three examples with their numerical simulations are employed to show the effectiveness of the theoretical results.

### MSC:

34D06 | Synchronization of solutions to ordinary differential equations |

90B10 | Deterministic network models in operations research |

34K50 | Stochastic functional-differential equations |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{X. Yang} and \textit{J. Cao}, Discrete Dyn. Nat. Soc. 2010, Article ID 416182, 21 p. (2010; Zbl 1198.34090)

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