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**Dynamical behaviors of impulsive stochastic reaction-diffusion neural networks with mixed time delays.**
*(English)*
Zbl 1246.35108

Summary: We discuss the dynamical behaviors of impulsive stochastic reaction-diffusion neural networks (ISRDNNs) with mixed time delays. By using a well-known \(L\)-operator differential inequality with mixed time delays and combining with the Lyapunov-Krasovkii functional approach, as well as linear matrix inequality (LMI) technique, some novel sufficient conditions are derived to ensure the existence, uniqueness, and global exponential stability of the periodic solutions for ISRDNNs with mixed time delays in the mean square sense. The obtained sufficient conditions depend on the reaction-diffusion terms. The results of this paper are new and improve some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena, and mixed time delays are considered. Finally, two numerical examples are provided to verify the usefulness of the obtained results.

### MSC:

35K57 | Reaction-diffusion equations |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |

35R60 | PDEs with randomness, stochastic partial differential equations |

### Keywords:

impulsive stochastic reaction-diffusion neural networks; Lyapunov-Krasovkii functional approach
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\textit{W. Zhang} et al., Abstr. Appl. Anal. 2012, Article ID 236562, 21 p. (2012; Zbl 1246.35108)

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### References:

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