{"title":"两个自适应耦合 Theta 神经元的协同进化动力学","authors":"Felix Augustsson, Erik Andreas Martens","doi":"arxiv-2407.01089","DOIUrl":null,"url":null,"abstract":"Natural and technological networks exhibit dynamics that can lead to complex\ncooperative behaviors, such as synchronization in coupled oscillators and\nrhythmic activity in neuronal networks. Understanding these collective dynamics\nis crucial for deciphering a range of phenomena from brain activity to power\ngrid stability. Recent interest in co-evolutionary networks has highlighted the\nintricate interplay between dynamics on and of the network with mixed time\nscales. Here, we explore the collective behavior of excitable oscillators in a\nsimple networks of two Theta neurons with adaptive coupling without\nself-interaction. Through a combination of bifurcation analysis and numerical\nsimulations, we seek to understand how the level of adaptivity in the coupling\nstrength, $a$, influences the dynamics. We first investigate the dynamics\npossible in the non-adaptive limit; our bifurcation analysis reveals stability\nregions of quiescence and spiking behaviors, where the spiking frequencies\nmode-lock in a variety of configurations. Second, as we increase the adaptivity\n$a$, we observe a widening of the associated Arnol'd tongues, which may overlap\nand give room for multi-stable configurations. For larger adaptivity, the\nmode-locked regions may further undergo a period-doubling cascade into chaos.\nOur findings contribute to the mathematical theory of adaptive networks and\noffer insights into the potential mechanisms underlying neuronal communication\nand synchronization.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"349 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Co-evolutionary dynamics for two adaptively coupled Theta neurons\",\"authors\":\"Felix Augustsson, Erik Andreas Martens\",\"doi\":\"arxiv-2407.01089\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Natural and technological networks exhibit dynamics that can lead to complex\\ncooperative behaviors, such as synchronization in coupled oscillators and\\nrhythmic activity in neuronal networks. Understanding these collective dynamics\\nis crucial for deciphering a range of phenomena from brain activity to power\\ngrid stability. Recent interest in co-evolutionary networks has highlighted the\\nintricate interplay between dynamics on and of the network with mixed time\\nscales. Here, we explore the collective behavior of excitable oscillators in a\\nsimple networks of two Theta neurons with adaptive coupling without\\nself-interaction. Through a combination of bifurcation analysis and numerical\\nsimulations, we seek to understand how the level of adaptivity in the coupling\\nstrength, $a$, influences the dynamics. We first investigate the dynamics\\npossible in the non-adaptive limit; our bifurcation analysis reveals stability\\nregions of quiescence and spiking behaviors, where the spiking frequencies\\nmode-lock in a variety of configurations. Second, as we increase the adaptivity\\n$a$, we observe a widening of the associated Arnol'd tongues, which may overlap\\nand give room for multi-stable configurations. For larger adaptivity, the\\nmode-locked regions may further undergo a period-doubling cascade into chaos.\\nOur findings contribute to the mathematical theory of adaptive networks and\\noffer insights into the potential mechanisms underlying neuronal communication\\nand synchronization.\",\"PeriodicalId\":501305,\"journal\":{\"name\":\"arXiv - PHYS - Adaptation and Self-Organizing Systems\",\"volume\":\"349 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Adaptation and Self-Organizing Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.01089\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.01089","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Co-evolutionary dynamics for two adaptively coupled Theta neurons
Natural and technological networks exhibit dynamics that can lead to complex
cooperative behaviors, such as synchronization in coupled oscillators and
rhythmic activity in neuronal networks. Understanding these collective dynamics
is crucial for deciphering a range of phenomena from brain activity to power
grid stability. Recent interest in co-evolutionary networks has highlighted the
intricate interplay between dynamics on and of the network with mixed time
scales. Here, we explore the collective behavior of excitable oscillators in a
simple networks of two Theta neurons with adaptive coupling without
self-interaction. Through a combination of bifurcation analysis and numerical
simulations, we seek to understand how the level of adaptivity in the coupling
strength, $a$, influences the dynamics. We first investigate the dynamics
possible in the non-adaptive limit; our bifurcation analysis reveals stability
regions of quiescence and spiking behaviors, where the spiking frequencies
mode-lock in a variety of configurations. Second, as we increase the adaptivity
$a$, we observe a widening of the associated Arnol'd tongues, which may overlap
and give room for multi-stable configurations. For larger adaptivity, the
mode-locked regions may further undergo a period-doubling cascade into chaos.
Our findings contribute to the mathematical theory of adaptive networks and
offer insights into the potential mechanisms underlying neuronal communication
and synchronization.