Abstract
We study the dynamics of a simple bistable system driven by multiplicative correlated noise. Such system mimics the dynamics of classical attractor neural networks with an additional source of noise associated, for instance, with the stochasticity of synaptic transmission. We found that the multiplicative noise, which performs as a fluctuating barrier separating the stable solutions, strongly influences the behaviour of the system, giving rise to complex time series and scale-free distributions for the escape times of the system. This finding may be of interest to understand nonlinear phenomena observed in real neural systems and to design bio-inspired artificial neural networks with convenient complex characteristics.
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
Amari, S.: Characteristics of random nets of analog neuron-like elements. IEEE Trans. Syst. Man. Cybern. 2, 643–657 (1972)
Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982)
Hebb, D.O.: The Organization of Behavior: A Neuropsychological Theory. Wiley, Chichester (1949)
Amit, D.J., Gutfreund, H., Sompolinsky, H.: Statistical mechanics of neural networks near saturation. Ann. Phys. 173, 30–67 (1987)
Mejias, J.F., Torres, J.J.: Maximum memory capacity on neural networks with short-term depression and facilitation. Neural Comp. 21(3), 851–871 (2009)
Johnson, S., Marro, J., Torres, J.J.: Functional optimization in complex excitable networks. Europhys. Lett. 83, 46006 (1–6) (2008)
Pantic, L., Torres, J.J., Kappen, H.J., Gielen, S.C.A.M.: Associative memmory with dynamic synapses. Neural Comput. 14, 2903–2923 (2002)
Torres, J.J., Cortes, J.M., Marro, J., Kappen, H.J.: Competition between synaptic depression and facilitation in attractor neural networks. Neural Comput. 19, 2739–2755 (2007)
Allen, C., Stevens, C.F.: An evaluation of causes for unreliability of synaptic transmission. Proc. Natl. Acad. Sci. USA 91, 10380–10383 (1994)
de la Rocha, J., Parga, N.: Short-term synaptic depression causes a non-monotonic response to correlated stimuli. J. Neurosci. 25(37), 8416–8431 (2005)
Mejias, J.F., Torres, J.J.: The role of synaptic facilitation in spike coincidence detection. J. Comp. Neurosci. 24(2), 222–234 (2008)
Madureira, A.J.R., Hanggi, P., Buonomano, V., Rodrigues Jr., W.A.: Escape from a fluctuating double well. Phys. Rev. E 51, 3849–3861 (1995)
Ya, J., Jia-rong, L., Yi-cheng, C.: A novel phase transition phenomenon in bistable system. Chin. Phys. Lett. 14, 245–247 (1997)
Can-Jun, W., Shi-Bo, C., Dong-Cheng, M.: Steady-state analysis of a bistable system subject to a coloured multiplicative noise and a white additive noise with coloured cross-correlated noises. Chin. Phys. 15, 1435–1440 (2006)
Torres, J.J., Mejias, J.F., Kappen, H.J.: Bistable neural dynamics driven by multiplicative colored noise (submitted)
Boucsein, C., Tetzlaff, T., Meier, R., Aertsen, A., Naundorf, B.: Dynamical response properties of neocortical neuron ensembles: multiplicative versus additive noise. J. Neurosci. 29, 1006–1010 (2009)
Chialvo, D.R.: Psychophysics: are our senses critical? Nat. Phys. 2, 301–302 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mejias, J.F., Torres, J.J., Johnson, S., Kappen, H.J. (2009). Switching Dynamics of Neural Systems in the Presence of Multiplicative Colored Noise. In: Cabestany, J., Sandoval, F., Prieto, A., Corchado, J.M. (eds) Bio-Inspired Systems: Computational and Ambient Intelligence. IWANN 2009. Lecture Notes in Computer Science, vol 5517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02478-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-02478-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02477-1
Online ISBN: 978-3-642-02478-8
eBook Packages: Computer ScienceComputer Science (R0)