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Lagrange \(p\)-Stability and Exponential \(p\)-Convergence for Stochastic Cohen–Grossberg Neural Networks with Time-Varying Delays

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Abstract

This paper focus on the problem of \(p\)-stability in Lagrange sense and exponential \(p\)-convergence for stochastic Cohen–Grossberg neural networks with time-varying delays. By using a delay \(\fancyscript{L}\)-operator differential inequality, and coupling with Lyapunov method and stochastic analysis techniques, some sufficient conditions are derived to guarantee Lagrange \(p\)-stability and the state variables of the discussed stochastic Cohen–Grossberg neural networks with time-varying delays to converge, globally, uniformly, exponentially to a ball in the state space with a pre-specified convergence rate. Meanwhile, the exponential \(p\)-convergent balls are also estimated. Here, the existence and uniqueness of the equilibrium point needs not to be considered. Finally, some examples with numerical simulations are given to illustrate the effectiveness of our theoretical results.

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Acknowledgments

The authors are grateful for the support of the National Natural Science Foundation of China (61174216, 61273183, 61304162), the Scientific Innovation Team Project of Hubei Provincial Department of Education (T200809) and the Graduate Scientific Research Foundation of China Three Gorges University (2014PY063).

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Authors and Affiliations

  1. College of Science, China Three Gorges University, Yichang, 443002, Hubei, China

    Liangliang Li & Jigui Jian

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  1. Liangliang Li
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Correspondence to Jigui Jian.

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Li, L., Jian, J. Lagrange \(p\)-Stability and Exponential \(p\)-Convergence for Stochastic Cohen–Grossberg Neural Networks with Time-Varying Delays. Neural Process Lett 43, 611–626 (2016). https://doi.org/10.1007/s11063-015-9433-6

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