The stability of the completely synchronous state in neural networks with electrical coupling is analytically investigated applying both the Master Stability Function approach (MSF), developed by Pecora and Carroll (1998), and the Connection Graph Stability method (CGS) proposed by Belykh et al. (2004). The local dynamics is described by Morris-Lecar model for spiking neurons and by Hindmarsh-Rose model in spike, burst, irregular spike and irregular burst regimes. The combined application of both CGS and MSF methods provides an efficient estimate of the synchronization thresholds, namely bounds for the coupling strength ranges in which the synchronous state is stable. In all the considered cases, we observe that high values of coupling strength tend to synchronize the system. Furthermore, we observe a correlation between the single node attractor and the local stability properties given by MSF. The analytical results are compared with numerical simulations on a sample network, with excellent agreement.
How single node dynamics enhances synchronization in neural networks with electrical coupling
A Vezzani
2016
Abstract
The stability of the completely synchronous state in neural networks with electrical coupling is analytically investigated applying both the Master Stability Function approach (MSF), developed by Pecora and Carroll (1998), and the Connection Graph Stability method (CGS) proposed by Belykh et al. (2004). The local dynamics is described by Morris-Lecar model for spiking neurons and by Hindmarsh-Rose model in spike, burst, irregular spike and irregular burst regimes. The combined application of both CGS and MSF methods provides an efficient estimate of the synchronization thresholds, namely bounds for the coupling strength ranges in which the synchronous state is stable. In all the considered cases, we observe that high values of coupling strength tend to synchronize the system. Furthermore, we observe a correlation between the single node attractor and the local stability properties given by MSF. The analytical results are compared with numerical simulations on a sample network, with excellent agreement.| Campo DC | Valore | Lingua |
|---|---|---|
| dc.authority.ancejournal | CHAOS, SOLITONS AND FRACTALS | - |
| dc.authority.orgunit | Istituto Nanoscienze - NANO | - |
| dc.authority.people | E Bonacini | it |
| dc.authority.people | R Burioni | it |
| dc.authority.people | M di Volo | it |
| dc.authority.people | M Groppi | it |
| dc.authority.people | C Soresina | it |
| dc.authority.people | A Vezzani | it |
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| dc.date.accessioned | 2024/02/21 09:21:14 | - |
| dc.date.available | 2024/02/21 09:21:14 | - |
| dc.date.issued | 2016 | - |
| dc.description.abstracteng | The stability of the completely synchronous state in neural networks with electrical coupling is analytically investigated applying both the Master Stability Function approach (MSF), developed by Pecora and Carroll (1998), and the Connection Graph Stability method (CGS) proposed by Belykh et al. (2004). The local dynamics is described by Morris-Lecar model for spiking neurons and by Hindmarsh-Rose model in spike, burst, irregular spike and irregular burst regimes. The combined application of both CGS and MSF methods provides an efficient estimate of the synchronization thresholds, namely bounds for the coupling strength ranges in which the synchronous state is stable. In all the considered cases, we observe that high values of coupling strength tend to synchronize the system. Furthermore, we observe a correlation between the single node attractor and the local stability properties given by MSF. The analytical results are compared with numerical simulations on a sample network, with excellent agreement. | - |
| dc.description.affiliations | Univ Parma, Dipartimento Matemat & Informat, Parco Area Sci 53-A, I-43124 Parma, Italy Univ Parma, Dipartimento Fis & Sci Terra, Viale GP Usberti 7-A, I-43124 Parma, Italy Ist Nazl Fis Nucl, Grp Collegato Parma, Parco Area Sci 7-A, I-43124 Parma, Italy Univ Florence, Ctr Interdipartimentale Studio Dinam Complesse, Via Sansone 1, I-50019 Florence, Italy Univ Milan, Dipartimento Matemat F Enriques, Via Cesare Saldini 50, I-20133 Milan, Italy CNR Ist Nanosci, S3, Via Campi 213-A, I-41125 Modena, Italy Ecole Normale Super, Grp Neural Theory, Dept Etud Cognit, 24 Rue Lhomond, F-75231 Paris, FranceIndiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA | - |
| dc.description.allpeople | E. Bonacini; R. Burioni; M. di Volo; M. Groppi; C. Soresina;A. Vezzani | - |
| dc.description.allpeopleoriginal | E. Bonacini, R. Burioni, M. di Volo, M. Groppi, C. Soresina, and A. Vezzani | - |
| dc.description.fulltext | none | en |
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| dc.identifier.doi | 10.1016/j.chaos.2016.01.009 | - |
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| dc.language.iso | eng | - |
| dc.relation.firstpage | 32 | - |
| dc.relation.lastpage | 43 | - |
| dc.relation.volume | 85 | - |
| dc.subject.keywords | Connection Graph Stability | - |
| dc.subject.keywords | Master Stability Function | - |
| dc.subject.keywords | Neural network | - |
| dc.subject.keywords | Synchronization | - |
| dc.subject.singlekeyword | Connection Graph Stability | * |
| dc.subject.singlekeyword | Master Stability Function | * |
| dc.subject.singlekeyword | Neural network | * |
| dc.subject.singlekeyword | Synchronization | * |
| dc.title | How single node dynamics enhances synchronization in neural networks with electrical coupling | en |
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| iris.scopus.extTitle | How single node dynamics enhances synchronization in neural networks with electrical coupling | - |
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| scopus.contributor.affiliation | Università di Parma | - |
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| scopus.contributor.surname | Bonacini | - |
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| scopus.contributor.surname | Soresina | - |
| scopus.contributor.surname | Vezzani | - |
| scopus.date.issued | 2016 | * |
| scopus.description.abstracteng | The stability of the completely synchronous state in neural networks with electrical coupling is analytically investigated applying both the Master Stability Function approach (MSF), developed by Pecora and Carroll (1998), and the Connection Graph Stability method (CGS) proposed by Belykh et al. (2004). The local dynamics is described by Morris-Lecar model for spiking neurons and by Hindmarsh-Rose model in spike, burst, irregular spike and irregular burst regimes. The combined application of both CGS and MSF methods provides an efficient estimate of the synchronization thresholds, namely bounds for the coupling strength ranges in which the synchronous state is stable. In all the considered cases, we observe that high values of coupling strength tend to synchronize the system. Furthermore, we observe a correlation between the single node attractor and the local stability properties given by MSF. The analytical results are compared with numerical simulations on a sample network, with excellent agreement. | * |
| scopus.description.allpeopleoriginal | Bonacini E.; Burioni R.; Di Volo M.; Groppi M.; Soresina C.; Vezzani A. | * |
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| scopus.relation.firstpage | 32 | * |
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| scopus.relation.volume | 85 | * |
| scopus.subject.keywords | Connection Graph Stability; Master Stability Function; Neural network; Synchronization; | * |
| scopus.title | How single node dynamics enhances synchronization in neural networks with electrical coupling | * |
| scopus.titleeng | How single node dynamics enhances synchronization in neural networks with electrical coupling | * |
| Appare nelle tipologie: | 01.01 Articolo in rivista | |
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