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Stability analysis of delayed cellular neural networks with and without noise perturbation

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Abstract

The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.

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Authors and Affiliations

  1. Department of Mathematics, Shaoxing University, Shaoxing, 312000, Zhejiang Province, P. R. China

    Xue-juan Zhang  (张雪娟)

  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Guan-xiang Wang  (王冠香)

  3. Guanghua School of Management, Peking University, Beijing, 100871, P. R. China

    Hua Liu  (刘华)

Authors
  1. Xue-juan Zhang  (张雪娟)
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  2. Guan-xiang Wang  (王冠香)
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  3. Hua Liu  (刘华)
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Corresponding author

Correspondence to Guan-xiang Wang  (王冠香).

Additional information

(Communicated by LIU Zeng-rong)

Project supported by the National Natural Science Foundation of China (No. 10771155) and the Special Foundation for the Authors of National Excellent Doctoral Dissertations of China (FANEDD)

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Zhang, Xj., Wang, Gx. & Liu, H. Stability analysis of delayed cellular neural networks with and without noise perturbation. Appl. Math. Mech.-Engl. Ed. 29, 1427–1438 (2008). https://doi.org/10.1007/s10483-008-1104-x

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  • DOI: https://doi.org/10.1007/s10483-008-1104-x

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Chinese Library Classification

2000 Mathematics Subject Classification

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