On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings
We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system whe...
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creator | Nair, Anjana S Ghosh, Indranil Fatoyinbo, Hammed O Muni, Sishu S |
description | We put forward the dynamical study of a novel higher-order small network of
Chialvo neurons arranged in a ring-star topology, with the neurons interacting
via linear diffusive couplings. This model is perceived to imitate the
nonlinear dynamical properties exhibited by a realistic nervous system where
the neurons transfer information through higher-order multi-body interactions.
We first analyze our model using the tools from nonlinear dynamics literature:
fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the
coexistence of chaotic attractors, and also an intriguing route to chaos
starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed
invariant curves, to ultimately chaos. We numerically observe the existence of
codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark
Sacker. We also qualitatively study the typical phase portraits of the system
and numerically quantify chaos and complexity using the 0-1 test and sample
entropy measure respectively. Finally, we study the collective behavior of the
neurons in terms of two synchronization measures: the cross-correlation
coefficient, and the Kuramoto order parameter. |
doi_str_mv | 10.48550/arxiv.2405.06000 |
format | Article |
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Chialvo neurons arranged in a ring-star topology, with the neurons interacting
via linear diffusive couplings. This model is perceived to imitate the
nonlinear dynamical properties exhibited by a realistic nervous system where
the neurons transfer information through higher-order multi-body interactions.
We first analyze our model using the tools from nonlinear dynamics literature:
fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the
coexistence of chaotic attractors, and also an intriguing route to chaos
starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed
invariant curves, to ultimately chaos. We numerically observe the existence of
codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark
Sacker. We also qualitatively study the typical phase portraits of the system
and numerically quantify chaos and complexity using the 0-1 test and sample
entropy measure respectively. Finally, we study the collective behavior of the
neurons in terms of two synchronization measures: the cross-correlation
coefficient, and the Kuramoto order parameter.</description><identifier>DOI: 10.48550/arxiv.2405.06000</identifier><language>eng</language><subject>Physics - Adaptation and Self-Organizing Systems ; Physics - Chaotic Dynamics</subject><creationdate>2024-05</creationdate><rights>http://creativecommons.org/licenses/by-nc-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2405.06000$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2405.06000$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Nair, Anjana S</creatorcontrib><creatorcontrib>Ghosh, Indranil</creatorcontrib><creatorcontrib>Fatoyinbo, Hammed O</creatorcontrib><creatorcontrib>Muni, Sishu S</creatorcontrib><title>On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings</title><description>We put forward the dynamical study of a novel higher-order small network of
Chialvo neurons arranged in a ring-star topology, with the neurons interacting
via linear diffusive couplings. This model is perceived to imitate the
nonlinear dynamical properties exhibited by a realistic nervous system where
the neurons transfer information through higher-order multi-body interactions.
We first analyze our model using the tools from nonlinear dynamics literature:
fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the
coexistence of chaotic attractors, and also an intriguing route to chaos
starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed
invariant curves, to ultimately chaos. We numerically observe the existence of
codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark
Sacker. We also qualitatively study the typical phase portraits of the system
and numerically quantify chaos and complexity using the 0-1 test and sample
entropy measure respectively. Finally, we study the collective behavior of the
neurons in terms of two synchronization measures: the cross-correlation
coefficient, and the Kuramoto order parameter.</description><subject>Physics - Adaptation and Self-Organizing Systems</subject><subject>Physics - Chaotic Dynamics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tOwzAURL1hgQofwAr_QMJN_cBeooiXVKmb7rqILrHdWLh2ZScB_p60sBppRmekQ8hdAzVXQsAD5m8_12sOogYJANdkv410HCwd_GGwuUrZ2EzLEUOwZaTZxwMtI2Ya7fiV8idNjraDxzCnpZpyioVO8cwY79xU_Gxpn6ZTWMByQ64chmJv_3NFdi_Pu_at2mxf39unTYXyESqDjqleguO8Ucb0rgGrtZBccESrebNsxjHHDUqtJWguFPRafUiGes0EW5H7v9uLXXfK_oj5pztbdhdL9gt2ZE3t</recordid><startdate>20240509</startdate><enddate>20240509</enddate><creator>Nair, Anjana S</creator><creator>Ghosh, Indranil</creator><creator>Fatoyinbo, Hammed O</creator><creator>Muni, Sishu S</creator><scope>ALA</scope><scope>GOX</scope></search><sort><creationdate>20240509</creationdate><title>On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings</title><author>Nair, Anjana S ; Ghosh, Indranil ; Fatoyinbo, Hammed O ; Muni, Sishu S</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a670-daf38c60f4418ddcf10e9956454aae941c60df3f4da6996094580c98b63a92353</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Physics - Adaptation and Self-Organizing Systems</topic><topic>Physics - Chaotic Dynamics</topic><toplevel>online_resources</toplevel><creatorcontrib>Nair, Anjana S</creatorcontrib><creatorcontrib>Ghosh, Indranil</creatorcontrib><creatorcontrib>Fatoyinbo, Hammed O</creatorcontrib><creatorcontrib>Muni, Sishu S</creatorcontrib><collection>arXiv Nonlinear Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Nair, Anjana S</au><au>Ghosh, Indranil</au><au>Fatoyinbo, Hammed O</au><au>Muni, Sishu S</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings</atitle><date>2024-05-09</date><risdate>2024</risdate><abstract>We put forward the dynamical study of a novel higher-order small network of
Chialvo neurons arranged in a ring-star topology, with the neurons interacting
via linear diffusive couplings. This model is perceived to imitate the
nonlinear dynamical properties exhibited by a realistic nervous system where
the neurons transfer information through higher-order multi-body interactions.
We first analyze our model using the tools from nonlinear dynamics literature:
fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the
coexistence of chaotic attractors, and also an intriguing route to chaos
starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed
invariant curves, to ultimately chaos. We numerically observe the existence of
codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark
Sacker. We also qualitatively study the typical phase portraits of the system
and numerically quantify chaos and complexity using the 0-1 test and sample
entropy measure respectively. Finally, we study the collective behavior of the
neurons in terms of two synchronization measures: the cross-correlation
coefficient, and the Kuramoto order parameter.</abstract><doi>10.48550/arxiv.2405.06000</doi><oa>free_for_read</oa></addata></record> |
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subjects | Physics - Adaptation and Self-Organizing Systems Physics - Chaotic Dynamics |
title | On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings |
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