The Bifurcating Neuron Network 1

Lee, G.; Farhat, Nabil H.

doi:10.1016/s0893-6080(00)00083-6

Cited by 75 publications

(36 citation statements)

References 47 publications

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“…Experimental observations and theoretical models endorse Freeman's suggestions [23], [24]. Chaos can also provide a mechanism to generate controllable noise that can push the state of the network out of spurious attractors [25], [26].…”

Section: B Coupling Of the Complex Processing Elementsmentioning

confidence: 71%

Self-Organization in a Parametrically Coupled Logistic Map Network: A Model for Information Processing in the Visual Cortex

Pashaie

Farhat

2009

IEEE Trans. Neural Netw.

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In this paper, a new model seeking to emulate the way the visual cortex processes information and interacts with subcortical areas to produce higher level brain functions is described. We developed a macroscopic approach that incorporates salient attributes of the cortex based on combining tools of nonlinear dynamics, information theory, and the known organizational and anatomical features of cortex. Justifications for this approach and demonstration of its effectiveness are presented. We also demonstrate certain capabilities of this model in producing efficient sparse representations and providing the cortical computational maps. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/477 Abstract-In this paper, a new model seeking to emulate the way the visual cortex processes information and interacts with subcortical areas to produce higher level brain functions is described. We developed a macroscopic approach that incorporates salient attributes of the cortex based on combining tools of nonlinear dynamics, information theory, and the known organizational and anatomical features of cortex. Justifications for this approach and demonstration of its effectiveness are presented. We also demonstrate certain capabilities of this model in producing efficient sparse representations and providing the cortical computational maps.

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Section: B Coupling Of the Complex Processing Elementsmentioning

confidence: 71%

Self-Organization in a Parametrically Coupled Logistic Map Network: A Model for Information Processing in the Visual Cortex

Pashaie

Farhat

2009

IEEE Trans. Neural Netw.

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“…We extended the original SRM to show the chaotic response by adding a background sinusoidal oscillation in the same way as the bifurcating neuron 8 and the chaotic pulse coupled neural network 4 . In the extended SRM, the background oscillation is added to the term :…”

Section: Chaotic-srmmentioning

confidence: 99%

“…Authors have studied the formation of the chaotic cell assembly in the chaotic cellular neural network (Chaotic-CNN), which is a two dimensional coupled network of the chaotic spike response model (Chaotic-SRM) 5,6 . The Chaotic-SRM is an extended spike response model 7 that exhibits a chaotic inter-spike interval by adding the background sinusoidal oscillation 4,8 . One fundamental goal of this study is to achieve the visual segmentation using the chaotic synchronization.…”

Section: Introductionmentioning

confidence: 99%

Synchronized Response to Grayscale Image Inputs in Chaotic Cellular Neural Network

Yamaguchi¹,

Kubo²

2015

JRNAL

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In this study, the synchronized response in the chaotic cellular neural network for a grayscale visual stimulus was investigated in the viewpoint of neural coding. Simple gradation patterns were used as visual stimuli and the synchronized response was analyzed by the correlation of the spike firing times. As a result, synchronized responses were observed for the neurons that had similar input values and formed chaotic cell assemblies. Each assembly was distinguished from the others in terms of cross-correlation.

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“…The bifurcating neuron (BN) is a simple switched dynamical system inspired by spiking neuron models [1][2][3][4][5][6]. Repeating integrate-and-fire behavior between a constant threshold and a periodic base signal, the BN can exhibit various chaotic/periodic phenomena.…”

Section: Introductionmentioning

confidence: 99%

“…Repeating integrate-and-fire behavior between a constant threshold and a periodic base signal, the BN can exhibit various chaotic/periodic phenomena. On the other hand, integrate-andfire neuron models have been applied to many engineering systems including associative memories [2], image processors [7], and communication systems [4,8]. In the spiking neuron models (incl.…”

Section: Introductionmentioning

confidence: 99%

A simple integrate-and-fire system and various super-stable periodic orbits

Takahashi

Saito

2018

NOLTA

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This paper studies super-stable periodic orbits and related phenomena in a simple switched dynamical system. The system repeats integrate-and-fire behavior between a constant threshold and a periodic base signal. The base signal consists of two components: the fundamental and higher frequency triangular signals. First, we demonstrate "chaos + chaos = order" such that the system exhibits chaos if the base signal is either of the two components whereas the system exhibits a super-stable periodic orbit if the base signal consists of both components. This phenomenon is confirmed experimentally and is explained theoretically. Second, we extract two key parameters and show that the system can exhibit a variety of super-stable periodic orbits. Applying a mapping procedure, existence regions of basic super-stable periodic orbits are calculated precisely.

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The Bifurcating Neuron Network 1

Cited by 75 publications

References 47 publications

Self-Organization in a Parametrically Coupled Logistic Map Network: A Model for Information Processing in the Visual Cortex

Self-Organization in a Parametrically Coupled Logistic Map Network: A Model for Information Processing in the Visual Cortex

Synchronized Response to Grayscale Image Inputs in Chaotic Cellular Neural Network

A simple integrate-and-fire system and various super-stable periodic orbits

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