Inference and chaos by a network of nonmonotonic neurons

Domínguez, David

doi:10.1103/physreve.54.4066

Cited by 10 publications

(10 citation statements)

References 23 publications

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“…5 (a three-neuron network, or 3NN). It is to be expected that the behavior of the network also depends on the signs of coupling weights w 13 and w 32 and on the type of the basic oscillation NN.…”

Section: Three-neuron Networkmentioning

confidence: 99%

“…Consequently, the network is examined for each combination of signs of coupling weights w 13 , w 32 and the type of the basic oscillation NN [30,31] …”

Section: Three-neuron Networkmentioning

confidence: 99%

“…Lipo Wang's group showed that an ANN exhibits a chaotic response if the external input varies in a stochastic way [18][19][20][21]. There are also analyses, from the viewpoint of statistical dynamics, of the occurrence of chaos in special network structures [13,14].…”

Section: Introductionmentioning

confidence: 99%

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Minimum constituents of chaos neural network composed of conventional neurons

Kawamura

Yoshida

Miura

2003

Electron Comm Jpn Pt III

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SUMMARYMany studies of the neural network with chaotic output have been presented. In most of these, however, a neuron model or a network model is specially prepared to realize the chaotic response, and few studies have been based on the conventional model. This paper considers a neural network based on the conventional neuron model, such as is used in the Hopfield and other neural networks, and discusses the oscillation phenomenon. It is shown theoretically and experimentally that the behavior of the network composed of two neurons is either convergence or periodic oscillation. Then the network composed of three neurons is examined experimentally, and it is shown that convergence, periodic oscillation, quasi-periodic oscillation, or chaos can occur. In other words, it is shown that the minimum configuration of a neural network based on the conventional neuron model that can generate chaos is a network composed of three neurons.

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Section: Three-neuron Networkmentioning

confidence: 99%

“…Consequently, the network is examined for each combination of signs of coupling weights w 13 , w 32 and the type of the basic oscillation NN [30,31] …”

Section: Three-neuron Networkmentioning

confidence: 99%

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Minimum constituents of chaos neural network composed of conventional neurons

Kawamura

Yoshida

Miura

2003

Electron Comm Jpn Pt III

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“…The authors pointed out the emergence of chaos as a consequence of the non-monotonicity. The categorization ability of extremely diluted, three-state, non-monotonic neural network was studied in [14,15]. A categorization phase, as well as a chaotic phase, was noticed.…”

Section: Introductionmentioning

confidence: 99%

Retrieval and chaos in extremely diluted non-monotonic neural networks

Mainieri

Erichsen

2002

Physica A: Statistical Mechanics and its Applications

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We discuss, in this paper, the dynamical properties of extremely diluted, non-monotonic neural networks. Assuming parallel updating and the Hebb prescription for the synaptic connections, a flow equation for the macroscopic overlap is derived. A rich dynamical phase diagram, was obtained, showing a stable retrieval phase, as well as a cycle two and chaotic behavior. Numerical simulations were performed, showing good agreement with analytical results. Furthermore, the simulations give an additional insight into the microscopic dynamical behavior during the chaotic phase. It is shown that the freezing of individual neuron states is related to the structure of chaotic attractors.

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“…the function that gives the state of the neuron as a function of the postsynaptic potential) have been presented [12][13][14][15]. The physiological justification of a nonmonotonic transfer function is ascribed to the fatigue of neurons after being exposed to a large post-synaptic input [16].…”

Section: Introductionmentioning

confidence: 99%