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**Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations.**
*(English)*
Zbl 1205.34108

Summary: A class of recurrent neural networks with time delay in the leakage term under impulsive perturbations is considered. First, a sufficient condition is given to ensure the global existence and uniqueness of the solution for the addressed neural networks by using the contraction mapping theorem. Then, we present some sufficient conditions to guarantee the existence, uniqueness and global asymptotic stability of the equilibrium point by using topological degree theory, Lyapunov-Kravsovskii functionals and some analysis techniques. The proposed results, which do not require the boundedness, differentiability and monotonicity of the activation functions, can easily be checked via the linear matrix inequality (LMI) control toolbox in MATLAB. Moreover, they indicate that the stability behavior of neural networks is very sensitive to the time delay in the leakage term. In the absence of leakage delay, the results obtained are also new results. Finally, two numerical examples are given to show the effectiveness of the proposed results.

### MSC:

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

34K45 | Functional-differential equations with impulses |

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

47N20 | Applications of operator theory to differential and integral equations |

34K20 | Stability theory of functional-differential equations |

### Keywords:

recurrent neural networks; global existence; global stability; impulsive perturbations; time-varying delay; leakage delay; linear matrix inequality (LMI)### Software:

Matlab
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XMLCite

\textit{X. Li} et al., Nonlinear Anal., Real World Appl. 11, No. 5, 4092--4108 (2010; Zbl 1205.34108)

Full Text:
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