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Global exponential convergence and global convergence in finite time of non-autonomous discontinuous neural networks

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Abstract

The paper investigates global convergence of the solutions of a non-autonomous differential system with discontinuous right-hand side, arising from the description of the states of neurons in a general class of neural networks possessing discontinuous neuron activations in a time-varying situation. By exploring intrinsic features between the non-autonomous system and its asymptotic system, several novel sufficient conditions are derived which ensure global exponential convergence of the networks. Moreover, under some conditions, we prove that this networks possesses the property of global convergence in finite time, which cannot occur in smooth system. Our results can be easily verified and complement previous known criteria.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, People’s Republic of China

    Zhenyuan Guo & Lihong Huang

Authors
  1. Zhenyuan Guo
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  2. Lihong Huang
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Correspondence to Lihong Huang.

Additional information

Research supported by National Natural Science Foundation of China (10771055, 60835004) and Key Program of Application Science Foundation of Hunan Province (2008FJ2008).

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Guo, Z., Huang, L. Global exponential convergence and global convergence in finite time of non-autonomous discontinuous neural networks. Nonlinear Dyn 58, 349–359 (2009). https://doi.org/10.1007/s11071-009-9483-2

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  • DOI: https://doi.org/10.1007/s11071-009-9483-2

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