Abstract
In this paper, discrete-time analogues of continuous-time neural networks with continuously distributed delays and periodic inputs are investigated without assuming Lipschitz conditions on the activation functions. The discrete-time analogues are considered to be numerical discretizations of the continuous-time networks and we study their dynamical characteristics. By employing Halanay-type inequality, we obtain easily verifiable sufficient conditions ensuring that every solutions of the discrete-time analogue converge exponentially to the unique periodic solutions. It is shown that the discrete-time analogues inherit the periodicity of the continuous-time networks. The results obtained can be regarded as a generalization to the discontinuous case of previous results established for delayed neural networks possessing smooth neuron activation.
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© 2005 Springer-Verlag Berlin Heidelberg
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Sun, C., Xia, L., Feng, C. (2005). Globally Attractive Periodic Solutions of Continuous-Time Neural Networks and Their Discrete-Time Counterparts. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_42
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DOI: https://doi.org/10.1007/11427391_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25912-1
Online ISBN: 978-3-540-32065-4
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