Approximating the stability region of a neural network with a general distribution of delays
We investigate the linear stability of a neural network with distributed delay, where the neurons are identical. We examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. We determine a...
Gespeichert in:
| Veröffentlicht in: | Neural networks 2010-12, Vol.23 (10), p.1187-1201 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1201 |
|---|---|
| container_issue | 10 |
| container_start_page | 1187 |
| container_title | Neural networks |
| container_volume | 23 |
| creator | Jessop, R. Campbell, S.A. |
| description | We investigate the linear stability of a neural network with distributed delay, where the neurons are identical. We examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are known. Finally, we compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments. |
| doi_str_mv | 10.1016/j.neunet.2010.06.009 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_849456972</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S089360801000122X</els_id><sourcerecordid>849456972</sourcerecordid><originalsourceid>FETCH-LOGICAL-c469t-d5f6beb7aba378d7d1c15a7aaeec81ca3f6d4a91435c28fed2ce772b956c8c4d3</originalsourceid><addsrcrecordid>eNqFkUtv1DAUhS0EaqePf4BQNohVhuvY8WNTqaqgIFViA7tKlmPfTD1kkqntUObf49EMsGtXVzr67uscQt5SWFKg4uN6OeI8Yl42UCQQSwD9iiyokrpupGpekwUozWoBCk7JWUprABCKsxNy2oDQouVqQe6vt9s4_Q4bm8O4qvIDVinbLgwh76qIqzCN1dRXtirLoh1KyU9T_Fk9hfxQ1BWOuJd9SDmGbs5H3uNgd-mCvOntkPDyWM_Jj8-fvt98qe--3X69ub6rHRc6177tRYedtJ1lUnnpqaOtldYiOkWdZb3w3GrKWesa1aNvHErZdLoVTjnu2Tn5cJhbXnmcMWWzCcnhMNgRpzkZxTVvhZbNi6RUEjiTmheSH0gXp5Qi9mYbi0txZyiYfQBmbQ4BmH0ABoQpAZS2d8cFc7dB_6_pr-MFeH8EbHJ26KMdXUj_OdYC18AKd3XgsBj3K2A0yQUcHfoQ0WXjp_D8JX8AXqSoCg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>787043794</pqid></control><display><type>article</type><title>Approximating the stability region of a neural network with a general distribution of delays</title><source>MEDLINE</source><source>Access via ScienceDirect (Elsevier)</source><creator>Jessop, R. ; Campbell, S.A.</creator><creatorcontrib>Jessop, R. ; Campbell, S.A.</creatorcontrib><description>We investigate the linear stability of a neural network with distributed delay, where the neurons are identical. We examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are known. Finally, we compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments.</description><identifier>ISSN: 0893-6080</identifier><identifier>EISSN: 1879-2782</identifier><identifier>DOI: 10.1016/j.neunet.2010.06.009</identifier><identifier>PMID: 20696548</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Algorithms ; Applied sciences ; Artificial Intelligence ; Computer science; control theory; systems ; Computer Simulation ; Connectionism. Neural networks ; Control system analysis ; Control theory. Systems ; Delay differential equations ; Delay independent stability ; Discrete delay ; Distributed delay ; Exact sciences and technology ; Linear stability ; Neural Networks (Computer) ; Neurons - physiology</subject><ispartof>Neural networks, 2010-12, Vol.23 (10), p.1187-1201</ispartof><rights>2010 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><rights>Copyright © 2010 Elsevier Ltd. All rights reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c469t-d5f6beb7aba378d7d1c15a7aaeec81ca3f6d4a91435c28fed2ce772b956c8c4d3</citedby><cites>FETCH-LOGICAL-c469t-d5f6beb7aba378d7d1c15a7aaeec81ca3f6d4a91435c28fed2ce772b956c8c4d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.neunet.2010.06.009$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23504903$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/20696548$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Jessop, R.</creatorcontrib><creatorcontrib>Campbell, S.A.</creatorcontrib><title>Approximating the stability region of a neural network with a general distribution of delays</title><title>Neural networks</title><addtitle>Neural Netw</addtitle><description>We investigate the linear stability of a neural network with distributed delay, where the neurons are identical. We examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are known. Finally, we compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Artificial Intelligence</subject><subject>Computer science; control theory; systems</subject><subject>Computer Simulation</subject><subject>Connectionism. Neural networks</subject><subject>Control system analysis</subject><subject>Control theory. Systems</subject><subject>Delay differential equations</subject><subject>Delay independent stability</subject><subject>Discrete delay</subject><subject>Distributed delay</subject><subject>Exact sciences and technology</subject><subject>Linear stability</subject><subject>Neural Networks (Computer)</subject><subject>Neurons - physiology</subject><issn>0893-6080</issn><issn>1879-2782</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFkUtv1DAUhS0EaqePf4BQNohVhuvY8WNTqaqgIFViA7tKlmPfTD1kkqntUObf49EMsGtXVzr67uscQt5SWFKg4uN6OeI8Yl42UCQQSwD9iiyokrpupGpekwUozWoBCk7JWUprABCKsxNy2oDQouVqQe6vt9s4_Q4bm8O4qvIDVinbLgwh76qIqzCN1dRXtirLoh1KyU9T_Fk9hfxQ1BWOuJd9SDmGbs5H3uNgd-mCvOntkPDyWM_Jj8-fvt98qe--3X69ub6rHRc6177tRYedtJ1lUnnpqaOtldYiOkWdZb3w3GrKWesa1aNvHErZdLoVTjnu2Tn5cJhbXnmcMWWzCcnhMNgRpzkZxTVvhZbNi6RUEjiTmheSH0gXp5Qi9mYbi0txZyiYfQBmbQ4BmH0ABoQpAZS2d8cFc7dB_6_pr-MFeH8EbHJ26KMdXUj_OdYC18AKd3XgsBj3K2A0yQUcHfoQ0WXjp_D8JX8AXqSoCg</recordid><startdate>20101201</startdate><enddate>20101201</enddate><creator>Jessop, R.</creator><creator>Campbell, S.A.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>7QO</scope><scope>7TK</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope></search><sort><creationdate>20101201</creationdate><title>Approximating the stability region of a neural network with a general distribution of delays</title><author>Jessop, R. ; Campbell, S.A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c469t-d5f6beb7aba378d7d1c15a7aaeec81ca3f6d4a91435c28fed2ce772b956c8c4d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Artificial Intelligence</topic><topic>Computer science; control theory; systems</topic><topic>Computer Simulation</topic><topic>Connectionism. Neural networks</topic><topic>Control system analysis</topic><topic>Control theory. Systems</topic><topic>Delay differential equations</topic><topic>Delay independent stability</topic><topic>Discrete delay</topic><topic>Distributed delay</topic><topic>Exact sciences and technology</topic><topic>Linear stability</topic><topic>Neural Networks (Computer)</topic><topic>Neurons - physiology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jessop, R.</creatorcontrib><creatorcontrib>Campbell, S.A.</creatorcontrib><collection>Pascal-Francis</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>Biotechnology Research Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><jtitle>Neural networks</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jessop, R.</au><au>Campbell, S.A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Approximating the stability region of a neural network with a general distribution of delays</atitle><jtitle>Neural networks</jtitle><addtitle>Neural Netw</addtitle><date>2010-12-01</date><risdate>2010</risdate><volume>23</volume><issue>10</issue><spage>1187</spage><epage>1201</epage><pages>1187-1201</pages><issn>0893-6080</issn><eissn>1879-2782</eissn><abstract>We investigate the linear stability of a neural network with distributed delay, where the neurons are identical. We examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are known. Finally, we compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><pmid>20696548</pmid><doi>10.1016/j.neunet.2010.06.009</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0893-6080 |
| ispartof | Neural networks, 2010-12, Vol.23 (10), p.1187-1201 |
| issn | 0893-6080 1879-2782 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_849456972 |
| source | MEDLINE; Access via ScienceDirect (Elsevier) |
| subjects | Algorithms Applied sciences Artificial Intelligence Computer science control theory systems Computer Simulation Connectionism. Neural networks Control system analysis Control theory. Systems Delay differential equations Delay independent stability Discrete delay Distributed delay Exact sciences and technology Linear stability Neural Networks (Computer) Neurons - physiology |
| title | Approximating the stability region of a neural network with a general distribution of delays |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-21T08%3A17%3A26IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Approximating%20the%20stability%20region%20of%20a%20neural%20network%20with%20a%20general%20distribution%20of%20delays&rft.jtitle=Neural%20networks&rft.au=Jessop,%20R.&rft.date=2010-12-01&rft.volume=23&rft.issue=10&rft.spage=1187&rft.epage=1201&rft.pages=1187-1201&rft.issn=0893-6080&rft.eissn=1879-2782&rft_id=info:doi/10.1016/j.neunet.2010.06.009&rft_dat=%3Cproquest_cross%3E849456972%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=787043794&rft_id=info:pmid/20696548&rft_els_id=S089360801000122X&rfr_iscdi=true |