Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches.

*(English)*Zbl 1264.93048Summary: In this paper, global dissipativity and quasi-synchronization issues are investigated for delayed neural networks with discontinuous activation functions. Under the framework of Filippov solutions, the existence and dissipativity of solutions can be guaranteed by the matrix measure approach and the new obtained generalized Halanay inequalities. Then, for the discontinuous master-response systems with parameter mismatches, quasi-synchronization criteria are obtained by using feedback control. Furthermore, when proper approximate functions are selected, the complete synchronization can be discussed as a special case that two systems are identical. Numerical simulations on the chaotic systems are presented to demonstrate the effectiveness of the theoretical results.

##### MSC:

93B35 | Sensitivity (robustness) |

93C15 | Control/observation systems governed by ordinary differential equations |

34D06 | Synchronization of solutions to ordinary differential equations |

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

##### Keywords:

quasi-synchronization; discontinuous activations; Filippov solutions; matrix measure; generalized Halanay inequalities
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\textit{X. Liu} et al., Neural Netw. 24, No. 10, 1013--1021 (2011; Zbl 1264.93048)

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