On the dynamics of analogue neurons with nonsigmoidal gain functions

Bollé, Désiré; Vinck, B

doi:10.1016/0378-4371(95)00341-x

Cited by 14 publications

(6 citation statements)

References 15 publications

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“…A similar result was recently found for the pure multistate model for retrieval of patterns, but using analog non-monotonic neurons instead of our discrete neurons [23]. This shows that the present complex behavior is rather a consequence of the non-monotonicity than a characteristic of the generalization model.…”

Section: Attractors and Conclusionsupporting

confidence: 88%

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Inference and chaos by a network of nonmonotonic neurons

Domínguez

1996

Phys. Rev. E

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The generalization properties of an attractive network of nonmonotonic neurons that infers concepts from samples are studied. The macroscopic dynamics for the overlap between the neuron states and concepts, as well as the activity of the neurons, is obtained and numerically studied. Complex behavior leading from fixed points to chaos through a cascade of bifurcation is found when we increase the correlation between samples, decrease the activity of the samples and the load of concepts, or tune the threshold of fatigue of the neurons. Both the information dimension and the Liapunov exponent are given and a phase diagram is built.

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Section: Attractors and Conclusionsupporting

confidence: 88%

“…The G phase is separated from the D phase by the dashed curve. Differently from the phase diagram obtained in [23], here no phase {Z : M = 0, Q = 0} can be reached, as can be seen from the Eq. ( 11), with m t = 0, which reads…”

Section: Attractors and Conclusioncontrasting

confidence: 62%

Inference and chaos by a network of nonmonotonic neurons

Domínguez

1996

Phys. Rev. E

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“…the transfer function that gives the state of the neuron as a function of the post-synaptic potential. In recent papers [16,17] it has been shown that such a nonmonotonic transfer function may lead to macroscopic chaos in attractor neural networks: chaos appears in a class of macroscopic trajectories characterized by an overlap with the initial configuration that never vanishes. In other words, the network preserves a memory of the initial configu-ration, but the macroscopic overlap does not converge to a fixed value and oscillates giving rise to a chaotic time series.…”

Section: Introductionmentioning

confidence: 99%

Chaos in neural networks with a nonmonotonic transfer function

et al. 1999

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Time evolution of diluted neural networks with a nonmonotonic transfer function is analytically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviors: fixed-point, periodicity, and chaos. We examine in detail the structure of the strange attractor and in particular we study the main features of the stable and unstable manifolds, the hyperbolicity of the attractor, and the existence of homoclinic intersections. We also discuss the problem of the robustness of the chaos and we prove that in the present model chaotic behavior is fragile (chaotic regions are densely intercalated with periodicity windows), according to a recently discussed conjecture. Finally we perform an analysis of the microscopic behavior and in particular we examine the occurrence of damage spreading by studying the time evolution of two almost identical initial configurations. We show that for any choice of the parameters the two initial states remain microscopically distinct.

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“…olfactory stimuli (Ashwin and Timme, 2005). Consequently, there has recently been some effort in incorporating constructive chaos in neural network modeling (Wang et al, 1990;Bolle and Vink, 1996;Dominguez and Theumann, 1997;Caroppo et al, 1999;Poon and Barahona, 2001;Mainieri and Jr., 2002;Katayama et al, 2003). Concluding on the significance of chaos in neurobiological systems is still an open issue (Rabinovich and Abarbanel, 1998;Faure and Korn, 2001;Korn and Faure, 2003), however.…”

Section: Introductionmentioning

confidence: 99%

Chaotic hopping between attractors in neural networks

2007

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We present a neurobiologically-inspired stochastic cellular automaton whose state jumps with time between the attractors corresponding to a series of stored patterns. The jumping varies from regular to chaotic as the model parameters are modified. The resulting irregular behavior, which mimics the state of attention in which a systems shows a great adaptability to changing stimulus, is a consequence in the model of shorttime presynaptic noise which induces synaptic depression. We discuss results from both a mean-field analysis and Monte Carlo simulations.

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On the dynamics of analogue neurons with nonsigmoidal gain functions

Cited by 14 publications

References 15 publications

Inference and chaos by a network of nonmonotonic neurons

Inference and chaos by a network of nonmonotonic neurons

Chaos in neural networks with a nonmonotonic transfer function

Chaotic hopping between attractors in neural networks

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