Abstract
We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks with the form of
, where the input-output function is defined as a generalized sigmoid function, such asv i =2/π arctan(π/2μiμi),\(v_i = \frac{2}{\pi }arctan\left( {\frac{\pi }{2}\mu _i u_i } \right)\) and\(v_i = \frac{1}{{1 + e^{ - u_i /\varepsilon } }},\), etc. Numerical simulations are also provided to demonstrate the theoretical results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Hopfield, J., Tank, D., Neural computation of decisions in optimization problems, Biological Cybernetics, 1985, 52: 141.
Hopfield, J., Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. USA, 1982, 79: 2554.
Chen, L., Aihara, K., Chaotic simulated annealing by a neural network model with transient chaos, Neural Networks, 1995. 8(6): 915.
Hopfield, J., Neurons with graded response have collective computational properties like those of two-state neurons, Pmc. Natl. Acad. Sci. USA, 1984, 81: 3088.
Li, J. H., Micheland, A. N., Porod, W., Qualitative analysis and synthesis of a class of neural networks, IEEE Trans. on Circuits and Systems, 1988, 35(8): 976.
Gopalsamy, K., He, X. Z., Stability in a symmetric Hopfield nets with transmission delays, Physica D, 1994, 76: 344.
Chen, L., Aihara, K., Chaos and asymptotic stability in discrete-time neural networks, Physica D, 1997, 104: 286.
Chen, L., Aihara, K., Global searching ability of chaotic neural networks, IEEE Trans. on Circuits and Systems-I: Fundamental Theory and Applications, 1999, 46(8): 974.
Tong, H., Non-linear Time Series-A Dynarnical System Approach, Oxford: Oxford University Press, 1990.
Hoppensteadt, F., Izhikevich, E., Weakly Connected Neural Networks, New York: Springer-Verlag, 1997.
Marotto, F. R., Snap-back repellers imply chaos inR η, J. Math. Anal. Appl., 1978, 63: 199.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, J., Chen, L. & Jing, Z. Chaos and asymptotical stability in discrete-time recurrent neural networks with generalized input-output function. Sci. China Ser. A-Math. 44, 193–200 (2001). https://doi.org/10.1007/BF02874421
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02874421