Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters

Neural circuits operate with delays over a range of time scales, from a few milliseconds in recurrent local circuitry to tens of milliseconds or more for communication between populations. Modeling usually incorporates single fixed delays, meant to represent the mean conduction delay between neurons...

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Autores principales:	S. Kamyar Tavakoli, André Longtin
Formato:	article
Lenguaje:	EN
Publicado:	Frontiers Media S.A. 2021
Materias:	dynamical system transient chaos delayed differential equation synchrony neural network neural dynamics Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571
Acceso en línea:	https://doaj.org/article/0f04e0990c964502bd94b23edf236cdb
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spelling	oai:doaj.org-article:0f04e0990c964502bd94b23edf236cdb2021-11-19T05:32:17ZComplexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters1662-513710.3389/fnsys.2021.720744https://doaj.org/article/0f04e0990c964502bd94b23edf236cdb2021-11-01T00:00:00Zhttps://www.frontiersin.org/articles/10.3389/fnsys.2021.720744/fullhttps://doaj.org/toc/1662-5137Neural circuits operate with delays over a range of time scales, from a few milliseconds in recurrent local circuitry to tens of milliseconds or more for communication between populations. Modeling usually incorporates single fixed delays, meant to represent the mean conduction delay between neurons making up the circuit. We explore conditions under which the inclusion of more delays in a high-dimensional chaotic neural network leads to a reduction in dynamical complexity, a phenomenon recently described as multi-delay complexity collapse (CC) in delay-differential equations with one to three variables. We consider a recurrent local network of 80% excitatory and 20% inhibitory rate model neurons with 10% connection probability. An increase in the width of the distribution of local delays, even to unrealistically large values, does not cause CC, nor does adding more local delays. Interestingly, multiple small local delays can cause CC provided there is a moderate global delayed inhibitory feedback and random initial conditions. CC then occurs through the settling of transient chaos onto a limit cycle. In this regime, there is a form of noise-induced order in which the mean activity variance decreases as the noise increases and disrupts the synchrony. Another novel form of CC is seen where global delayed feedback causes “dropouts,” i.e., epochs of low firing rate network synchrony. Their alternation with epochs of higher firing rate asynchrony closely follows Poisson statistics. Such dropouts are promoted by larger global feedback strength and delay. Finally, periodic driving of the chaotic regime with global feedback can cause CC; the extinction of chaos can outlast the forcing, sometimes permanently. Our results suggest a wealth of phenomena that remain to be discovered in networks with clusters of delays.S. Kamyar TavakoliAndré LongtinFrontiers Media S.A.articledynamical systemtransient chaosdelayed differential equationsynchronyneural networkneural dynamicsNeurosciences. Biological psychiatry. NeuropsychiatryRC321-571ENFrontiers in Systems Neuroscience, Vol 15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	dynamical system transient chaos delayed differential equation synchrony neural network neural dynamics Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571
spellingShingle	dynamical system transient chaos delayed differential equation synchrony neural network neural dynamics Neurosciences. Biological psychiatry. Neuropsychiatry RC321-571 S. Kamyar Tavakoli André Longtin Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters
description	Neural circuits operate with delays over a range of time scales, from a few milliseconds in recurrent local circuitry to tens of milliseconds or more for communication between populations. Modeling usually incorporates single fixed delays, meant to represent the mean conduction delay between neurons making up the circuit. We explore conditions under which the inclusion of more delays in a high-dimensional chaotic neural network leads to a reduction in dynamical complexity, a phenomenon recently described as multi-delay complexity collapse (CC) in delay-differential equations with one to three variables. We consider a recurrent local network of 80% excitatory and 20% inhibitory rate model neurons with 10% connection probability. An increase in the width of the distribution of local delays, even to unrealistically large values, does not cause CC, nor does adding more local delays. Interestingly, multiple small local delays can cause CC provided there is a moderate global delayed inhibitory feedback and random initial conditions. CC then occurs through the settling of transient chaos onto a limit cycle. In this regime, there is a form of noise-induced order in which the mean activity variance decreases as the noise increases and disrupts the synchrony. Another novel form of CC is seen where global delayed feedback causes “dropouts,” i.e., epochs of low firing rate network synchrony. Their alternation with epochs of higher firing rate asynchrony closely follows Poisson statistics. Such dropouts are promoted by larger global feedback strength and delay. Finally, periodic driving of the chaotic regime with global feedback can cause CC; the extinction of chaos can outlast the forcing, sometimes permanently. Our results suggest a wealth of phenomena that remain to be discovered in networks with clusters of delays.
format	article
author	S. Kamyar Tavakoli André Longtin
author_facet	S. Kamyar Tavakoli André Longtin
author_sort	S. Kamyar Tavakoli
title	Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters
title_short	Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters
title_full	Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters
title_fullStr	Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters
title_full_unstemmed	Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters
title_sort	complexity collapse, fluctuating synchrony, and transient chaos in neural networks with delay clusters
publisher	Frontiers Media S.A.
publishDate	2021
url	https://doaj.org/article/0f04e0990c964502bd94b23edf236cdb
work_keys_str_mv	AT skamyartavakoli complexitycollapsefluctuatingsynchronyandtransientchaosinneuralnetworkswithdelayclusters AT andrelongtin complexitycollapsefluctuatingsynchronyandtransientchaosinneuralnetworkswithdelayclusters
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Complexity Collapse, Fluctuating Synchrony, and Transient Chaos in Neural Networks With Delay Clusters

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