{"title":"Stochastic bursting in networks of excitable units with delayed coupling.","authors":"Chunming Zheng, Arkady Pikovsky","doi":"10.1007/s00422-021-00883-9","DOIUrl":null,"url":null,"abstract":"<p><p>We investigate the phenomenon of stochastic bursting in a noisy excitable unit with multiple weak delay feedbacks, by virtue of a directed tree lattice model. We find statistical properties of the appearing sequence of spikes and expressions for the power spectral density. This simple model is extended to a network of three units with delayed coupling of a star type. We find the power spectral density of each unit and the cross-spectral density between any two units. The basic assumptions behind the analytical approach are the separation of timescales, allowing for a description of the spike train as a point process, and weakness of coupling, allowing for a representation of the action of overlapped spikes via the sum of the one-spike excitation probabilities.</p>","PeriodicalId":55374,"journal":{"name":"Biological Cybernetics","volume":"116 2","pages":"121-128"},"PeriodicalIF":1.6000,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00422-021-00883-9","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Biological Cybernetics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s00422-021-00883-9","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/6/28 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"COMPUTER SCIENCE, CYBERNETICS","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the phenomenon of stochastic bursting in a noisy excitable unit with multiple weak delay feedbacks, by virtue of a directed tree lattice model. We find statistical properties of the appearing sequence of spikes and expressions for the power spectral density. This simple model is extended to a network of three units with delayed coupling of a star type. We find the power spectral density of each unit and the cross-spectral density between any two units. The basic assumptions behind the analytical approach are the separation of timescales, allowing for a description of the spike train as a point process, and weakness of coupling, allowing for a representation of the action of overlapped spikes via the sum of the one-spike excitation probabilities.
期刊介绍：
Biological Cybernetics is an interdisciplinary medium for theoretical and application-oriented aspects of information processing in organisms, including sensory, motor, cognitive, and ecological phenomena. Topics covered include: mathematical modeling of biological systems; computational, theoretical or engineering studies with relevance for understanding biological information processing; and artificial implementation of biological information processing and self-organizing principles. Under the main aspects of performance and function of systems, emphasis is laid on communication between life sciences and technical/theoretical disciplines.
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