Pulse-Coupled Decentral Synchronization

Mathar, Rudolf; Mattfeldt, J.

doi:10.1137/s0036139994278135

Cited by 65 publications

(58 citation statements)

References 4 publications

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“…• Firing Maps: Analysis of strongly pulse-coupled networks can be reduced to an analysis of a firing mapping. The theory is based on the Poincaré return maps, and was first introduced by Mirollo and Strogatz [28]; see also [8], [25], and [29].…”

Section: B Review Of Methodsmentioning

confidence: 99%

“…Whenever changes signs implies that the effect of firing of the th neuron onto the th neuron depends on the relative timing of their firing. If in the system (25), and just fired ( ), then a firing of delays the next firing of . In contrast, if is about to fire a spike ( ), then firing of the th neuron advances this event.…”

Section: A Instantaneous Synaptic Transmissionmentioning

confidence: 99%

“…This occurs in many biophysically detailed Hodgkin-Huxley-type models. System (26) exhibits essentially the same behavior as (25), but the connection function is continuous and . Such network does not have nasty problems associated with discontinuities, such as nonuniqueness of solutions; see Section IV-B.…”

Section: A Instantaneous Synaptic Transmissionmentioning

confidence: 99%

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Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory

Izhikevich

1999

IEEE Trans. Neural Netw.

201

124

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Abstract-We study pulse-coupled neural networks that satisfy only two assumptions: each isolated neuron fires periodically, and the neurons are weakly connected. Each such network can be transformed by a piece-wise continuous change of variables into a phase model, whose synchronization behavior and oscillatory associative properties are easier to analyze and understand. Using the phase model, we can predict whether a given pulse-coupled network has oscillatory associative memory, or what minimal adjustments should be made so that it can acquire memory. In the search for such minimal adjustments we obtain a large class of simple pulse-coupled neural networks that can memorize and reproduce synchronized temporal patterns the same way a Hopfield network does with static patterns. The learning occurs via modification of synaptic weights and/or synaptic transmission delays.Index Terms-Canonical models, Class 1 neural excitability, integrate-and-fire neurons, multiplexing, syn-fire chain, transmission delay.

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Section: B Review Of Methodsmentioning

confidence: 99%

Section: A Instantaneous Synaptic Transmissionmentioning

confidence: 99%

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Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory

Izhikevich

1999

IEEE Trans. Neural Netw.

201

124

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“…Prominent examples include self-organizing algorithms for time synchronization in wireless systems [27], resource scheduling [28], reducing energy consumption in sensor networks [29], and traffic light control systems [30].…”

Section: Wireless Communications: Application Of Coupled Oscillatorsmentioning

confidence: 99%

“…These delays make the synchronization scheme unstable, as nodes might receive "echos" of their own firing pulse. To regain stability, a refractory period can be introduced during which nodes do not increase their phase function [31,27]. Second, wireless communication technologies do typically not allow us to send infinitely short pulses over the air.…”

Section: Wireless Communications: Application Of Coupled Oscillatorsmentioning

confidence: 99%

A Survey of Models and Design Methods for Self-organizing Networked Systems

Elmenreich

D’Souza

Bettstetter

et al. 2009

Self-Organizing Systems

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Abstract. Self-organization, whereby through purely local interactions, global order and structure emerge, is studied broadly across many fields of science, economics, and engineering. We review several existing methods and modeling techniques used to understand self-organization in a general manner. We then present implementation concepts and case studies for applying these principles for the design and deployment of robust self-organizing networked systems.

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Self-Stabilizing Pulse Synchronization Inspired by Biological Pacemaker Networks

Daliot

Dolev

Parnas

2003

Lecture Notes in Computer Science

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We define the "Pulse Synchronization" problem that requires nodes to achieve tight synchronization of regular pulse events, in the settings of distributed computing systems. Pulse-coupled synchronization is a phenomenon displayed by a large variety of biological systems, typically overcoming a high level of noise. Inspired by such biological models, a robust and selfstabilizing Byzantine pulse synchronization algorithm for distributed computer systems is presented. The algorithm attains near optimal synchronization tightness while tolerating up to a third of the nodes exhibiting Byzantine behavior concurrently. Pulse synchronization has been previously shown to be a powerful building block for designing algorithms in this severe fault model. We have previously shown how to stabilize general Byzantine algorithms, using pulse synchronization. To the best of our knowledge there is no other scheme to do this without the use of synchronized pulses.

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Pulse-Coupled Decentral Synchronization

Cited by 65 publications

References 4 publications

Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory

Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory

A Survey of Models and Design Methods for Self-organizing Networked Systems

Self-Stabilizing Pulse Synchronization Inspired by Biological Pacemaker Networks

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