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**Novel stability criteria for impulsive delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincaré inequality.**
*(English)*
Zbl 1267.35026

Summary: This work is devoted to the investigation of stability theory for impulsive delayed reaction-diffusion Cohen-Grossberg neural networks with Dirichlet boundary condition. By means of Hardy-Poincarè inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring global exponential stability of the equilibrium point. The presented stability criteria show that not only reaction-diffusion coefficients but also regional features as well as the first eigenvalue of the Dirichlet Laplacian will impact the stability. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.

### MSC:

35B35 | Stability in context of PDEs |

35K57 | Reaction-diffusion equations |

35K51 | Initial-boundary value problems for second-order parabolic systems |

35R10 | Partial functional-differential equations |

### Keywords:

Dirichlet boundary condition; Hardy-Poincarè inequality; Gronwall-Bellman-type impulsive integral inequality
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\textit{Y. Zhang} and \textit{Q. Luo}, Chaos Solitons Fractals 45, No. 8, 1033--1040 (2012; Zbl 1267.35026)

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### References:

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