Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia
We study the emergence of phase-locking for Winfree oscillators under the effect of inertia. It is known that in a large coupling regime, oscillators governed by the deterministic second-order Winfree model with inertia converge to a unique equilibrium. In contrast, in this paper we show the asympto...
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| creator | Kang, Myeongju Rehmeier, Marco |
| description | We study the emergence of phase-locking for Winfree oscillators under the
effect of inertia. It is known that in a large coupling regime, oscillators
governed by the deterministic second-order Winfree model with inertia converge
to a unique equilibrium. In contrast, in this paper we show the asymptotic
emergence of non-trivial synchronization in a suitably small coupling regime.
Moreover, we study the effect of a new stochastically perturbed Winfree system
with multiplicative noise and obtain lower estimates in probability for the
pathwise emergence of such a synchronizing pattern, provided the noise is
sufficiently small. We also provide numerical simulations which hint at the
possibility of more general and stronger analytical results. |
| doi_str_mv | 10.48550/arxiv.2205.13844 |
| format | Article |
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effect of inertia. It is known that in a large coupling regime, oscillators
governed by the deterministic second-order Winfree model with inertia converge
to a unique equilibrium. In contrast, in this paper we show the asymptotic
emergence of non-trivial synchronization in a suitably small coupling regime.
Moreover, we study the effect of a new stochastically perturbed Winfree system
with multiplicative noise and obtain lower estimates in probability for the
pathwise emergence of such a synchronizing pattern, provided the noise is
sufficiently small. We also provide numerical simulations which hint at the
possibility of more general and stronger analytical results.</description><identifier>DOI: 10.48550/arxiv.2205.13844</identifier><language>eng</language><subject>Mathematics - Classical Analysis and ODEs ; Mathematics - Dynamical Systems ; Mathematics - Probability</subject><creationdate>2022-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</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/2205.13844$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2205.13844$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kang, Myeongju</creatorcontrib><creatorcontrib>Rehmeier, Marco</creatorcontrib><title>Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia</title><description>We study the emergence of phase-locking for Winfree oscillators under the
effect of inertia. It is known that in a large coupling regime, oscillators
governed by the deterministic second-order Winfree model with inertia converge
to a unique equilibrium. In contrast, in this paper we show the asymptotic
emergence of non-trivial synchronization in a suitably small coupling regime.
Moreover, we study the effect of a new stochastically perturbed Winfree system
with multiplicative noise and obtain lower estimates in probability for the
pathwise emergence of such a synchronizing pattern, provided the noise is
sufficiently small. We also provide numerical simulations which hint at the
possibility of more general and stronger analytical results.</description><subject>Mathematics - Classical Analysis and ODEs</subject><subject>Mathematics - Dynamical Systems</subject><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tqwzAURLXpoqT9gK6qH7BrPWxLyxLSBwS6CWRXcyVdJSK2FSTRx9-3TrsahjkMHELuWFNL1bbNA6Sv8FFz3rQ1E0rKa_K-mTAdcLZIo6fnI2SsxmhP6GguUDBTHxMF6rBgmsIccgmWwrzM0f7iS92H2SdEOkWHI_0M5UjDjKkEuCFXHsaMt_-5IrunzW79Um3fnl_Xj9sKul5WqI3j1oF1yjHP0UvJlfbQGc-QNxoFk76zrW4s00bIXvRG9iCY8gqM4WJF7v9uL4LDOYUJ0vewiA4XUfEDrvpP1A</recordid><startdate>20220527</startdate><enddate>20220527</enddate><creator>Kang, Myeongju</creator><creator>Rehmeier, Marco</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220527</creationdate><title>Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia</title><author>Kang, Myeongju ; Rehmeier, Marco</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-e9bd2cdacd8d1f2ef44289fa6bf1e209e314f6c590c19b34737b47a318f8abb23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Classical Analysis and ODEs</topic><topic>Mathematics - Dynamical Systems</topic><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Kang, Myeongju</creatorcontrib><creatorcontrib>Rehmeier, Marco</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kang, Myeongju</au><au>Rehmeier, Marco</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia</atitle><date>2022-05-27</date><risdate>2022</risdate><abstract>We study the emergence of phase-locking for Winfree oscillators under the
effect of inertia. It is known that in a large coupling regime, oscillators
governed by the deterministic second-order Winfree model with inertia converge
to a unique equilibrium. In contrast, in this paper we show the asymptotic
emergence of non-trivial synchronization in a suitably small coupling regime.
Moreover, we study the effect of a new stochastically perturbed Winfree system
with multiplicative noise and obtain lower estimates in probability for the
pathwise emergence of such a synchronizing pattern, provided the noise is
sufficiently small. We also provide numerical simulations which hint at the
possibility of more general and stronger analytical results.</abstract><doi>10.48550/arxiv.2205.13844</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Classical Analysis and ODEs Mathematics - Dynamical Systems Mathematics - Probability |
| title | Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia |
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