Abstract
The parametrically coupled map lattice (PCML) exhibits many interesting dynamical behaviors that are reminiscent of the adaptation and the learning of the neural network. In order for the PCML to be a model of the neural network, however, it is necessary to identify the biological counterpart of one-dimensional maps that constitute the PCML. One of the possible candidates is a netlet, a small population of randomly interconnected neurons, that was suggested to be a functional unit constituting the neural network. We studied the possibility of representing a netlet by a chaotic one-dimensional map and the result is the chaotic netlet map that we introduce in this paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kaneko, K.: Theory and Applications of Coupled Map Lattices. John Wiley & Sons, Chichester (1993)
Farhat, N.H., Hernandez, E.D.M., Lee, G.: Strategies for autonomous adaptation and learning in dynamical networks. In: Cabestany, J., Mira, J., Moreno-Díaz, R. (eds.) IWANN 1997. LNCS, vol. 1240, pp. 417–426. Springer, Heidelberg (1997)
Lee, G., Farhat, N.H.: Parametrically coupled sine map networks. International Journal of Bifurcation and Chaos 11, 1815–1834 (2001)
Aihara, K., Takabe, T., Toyoda, M.: Chaotic neural networks. Physics Letters A 144, 333–340 (1990)
Farhat, N.H., Eldefrawy, M.: The bifurcating neuron. In: Digest Annual OSA Meeting, San Jose, CA, pp. 10–10 (1991)
Harth, E.M., Csermely, T.J., Beek, B., Lindsay, R.D.: Brain functions and neural dynamics. Journal of Theoretical Biology 26, 93–120 (1970)
Anninos, P.A., Beek, B., Csermely, T.J., Harth, E.M., Pertile, G.: Dynamics of neural structures. Journal of Theoretical Biology 26, 121–148 (1970)
Hilborn, R.C.: Chaos and Nonlinear Dynamics. Oxford University Press, New York (1994)
Usher, M., Schuster, H.G., Niebur, E.: Dynamics of populations of integrated-and-fire neurons, partial synchronization and memory. Neural Computation 5, 570–586 (1993)
May, R.M.: Simple mathematical models with very complicated dynamics. Nature 26, 459–467 (1976)
Nicholls, J.G., Martin, A.R., Wallace, B.G.: From Neuron to Brain, 3rd edn. Sinauer, Sunderland (1992)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Lee, G., Yi, GS. (2007). The Chaotic Netlet Map. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72393-6_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-72393-6_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72392-9
Online ISBN: 978-3-540-72393-6
eBook Packages: Computer ScienceComputer Science (R0)