Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field
Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete‐time fractional‐order complex‐valued neural networks with time del...
Gespeichert in:
| Veröffentlicht in: | Mathematical methods in the applied sciences 2021-01, Vol.44 (1), p.419-440 |
|---|---|
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 440 |
|---|---|
| container_issue | 1 |
| container_start_page | 419 |
| container_title | Mathematical methods in the applied sciences |
| container_volume | 44 |
| creator | Pratap, Anbalagan Raja, Ramachandran Cao, Jinde Huang, Chuangxia Niezabitowski, Michal Bagdasar, Ovidiu |
| description | Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete‐time fractional‐order complex‐valued neural networks with time delays. When the fractional‐order β holds 1 |
| doi_str_mv | 10.1002/mma.6745 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2465901374</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2465901374</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2935-ecfe40cfae9160e6c04a2670318c12fbd24bfbb2afe26f0ff7d6dc903d77bad63</originalsourceid><addsrcrecordid>eNp1kM1KAzEUhYMoWKvgIwTcuJl6k0mTzrIU_6DFhboOmeQGUjOdmkyp3fkIPqNP4tS6dXW4h4_D5SPkksGIAfCbpjEjqcT4iAwYVFXBhJLHZABMQSE4E6fkLOclAEwY4wOinztThxi6HW09dSHbhB1-f351oUHqk7FdaFcm9k2bHCa67_vDYTQ7dHSFm2RiH922TW-ZhhW1bbOO-EF9wOjOyYk3MePFXw7J693ty-yhmD_dP86m88LyqhwXaD0KsN5gxSSgtCAMlwpKNrGM-9pxUfu65sYjlx68V046W0HplKqNk-WQXB1216l932Du9LLdpP7xrLmQ4wpYqURPXR8om9qcE3q9TqExaacZ6L0-3evTe309WhzQbYi4-5fTi8X0l_8BR9t2GQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2465901374</pqid></control><display><type>article</type><title>Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field</title><source>Wiley Online Library Journals Frontfile Complete</source><creator>Pratap, Anbalagan ; Raja, Ramachandran ; Cao, Jinde ; Huang, Chuangxia ; Niezabitowski, Michal ; Bagdasar, Ovidiu</creator><creatorcontrib>Pratap, Anbalagan ; Raja, Ramachandran ; Cao, Jinde ; Huang, Chuangxia ; Niezabitowski, Michal ; Bagdasar, Ovidiu</creatorcontrib><description>Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete‐time fractional‐order complex‐valued neural networks with time delays. When the fractional‐order β holds 1 < β < 2, sufficient criteria based on a discrete version of generalized Gronwall inequality and rising function property are established for ensuring the finite stability of addressing fractional‐order discrete‐time‐delayed complex‐valued neural networks (FODCVNNs). In the meanwhile, when the fractional‐order β holds 0 < β < 1, a global Mittag–Leffler stability criterion of a class of FODCVNNs is demonstrated with two classes of neuron activation function by means of two different new inequalities, fractional‐order discrete‐time Lyapunov method, discrete version Laplace transforms as well as a discrete version of Mittag–Leffler function. Finally, computer simulations of two numerical examples are illustrated to the correctness and effectiveness of the presented stability results.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.6745</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>complex‐valued neural networks ; discrete time ; finite‐time stability ; fractional‐order ; Laplace transforms ; Mittag–Leffler stability ; Neural networks ; Stability criteria</subject><ispartof>Mathematical methods in the applied sciences, 2021-01, Vol.44 (1), p.419-440</ispartof><rights>2020 John Wiley & Sons, Ltd.</rights><rights>2021 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2935-ecfe40cfae9160e6c04a2670318c12fbd24bfbb2afe26f0ff7d6dc903d77bad63</citedby><cites>FETCH-LOGICAL-c2935-ecfe40cfae9160e6c04a2670318c12fbd24bfbb2afe26f0ff7d6dc903d77bad63</cites><orcidid>0000-0002-0732-226X ; 0000-0003-4553-5351 ; 0000-0003-3133-7119</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.6745$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.6745$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Pratap, Anbalagan</creatorcontrib><creatorcontrib>Raja, Ramachandran</creatorcontrib><creatorcontrib>Cao, Jinde</creatorcontrib><creatorcontrib>Huang, Chuangxia</creatorcontrib><creatorcontrib>Niezabitowski, Michal</creatorcontrib><creatorcontrib>Bagdasar, Ovidiu</creatorcontrib><title>Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field</title><title>Mathematical methods in the applied sciences</title><description>Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete‐time fractional‐order complex‐valued neural networks with time delays. When the fractional‐order β holds 1 < β < 2, sufficient criteria based on a discrete version of generalized Gronwall inequality and rising function property are established for ensuring the finite stability of addressing fractional‐order discrete‐time‐delayed complex‐valued neural networks (FODCVNNs). In the meanwhile, when the fractional‐order β holds 0 < β < 1, a global Mittag–Leffler stability criterion of a class of FODCVNNs is demonstrated with two classes of neuron activation function by means of two different new inequalities, fractional‐order discrete‐time Lyapunov method, discrete version Laplace transforms as well as a discrete version of Mittag–Leffler function. Finally, computer simulations of two numerical examples are illustrated to the correctness and effectiveness of the presented stability results.</description><subject>complex‐valued neural networks</subject><subject>discrete time</subject><subject>finite‐time stability</subject><subject>fractional‐order</subject><subject>Laplace transforms</subject><subject>Mittag–Leffler stability</subject><subject>Neural networks</subject><subject>Stability criteria</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KAzEUhYMoWKvgIwTcuJl6k0mTzrIU_6DFhboOmeQGUjOdmkyp3fkIPqNP4tS6dXW4h4_D5SPkksGIAfCbpjEjqcT4iAwYVFXBhJLHZABMQSE4E6fkLOclAEwY4wOinztThxi6HW09dSHbhB1-f351oUHqk7FdaFcm9k2bHCa67_vDYTQ7dHSFm2RiH922TW-ZhhW1bbOO-EF9wOjOyYk3MePFXw7J693ty-yhmD_dP86m88LyqhwXaD0KsN5gxSSgtCAMlwpKNrGM-9pxUfu65sYjlx68V046W0HplKqNk-WQXB1216l932Du9LLdpP7xrLmQ4wpYqURPXR8om9qcE3q9TqExaacZ6L0-3evTe309WhzQbYi4-5fTi8X0l_8BR9t2GQ</recordid><startdate>20210115</startdate><enddate>20210115</enddate><creator>Pratap, Anbalagan</creator><creator>Raja, Ramachandran</creator><creator>Cao, Jinde</creator><creator>Huang, Chuangxia</creator><creator>Niezabitowski, Michal</creator><creator>Bagdasar, Ovidiu</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0002-0732-226X</orcidid><orcidid>https://orcid.org/0000-0003-4553-5351</orcidid><orcidid>https://orcid.org/0000-0003-3133-7119</orcidid></search><sort><creationdate>20210115</creationdate><title>Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field</title><author>Pratap, Anbalagan ; Raja, Ramachandran ; Cao, Jinde ; Huang, Chuangxia ; Niezabitowski, Michal ; Bagdasar, Ovidiu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2935-ecfe40cfae9160e6c04a2670318c12fbd24bfbb2afe26f0ff7d6dc903d77bad63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>complex‐valued neural networks</topic><topic>discrete time</topic><topic>finite‐time stability</topic><topic>fractional‐order</topic><topic>Laplace transforms</topic><topic>Mittag–Leffler stability</topic><topic>Neural networks</topic><topic>Stability criteria</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pratap, Anbalagan</creatorcontrib><creatorcontrib>Raja, Ramachandran</creatorcontrib><creatorcontrib>Cao, Jinde</creatorcontrib><creatorcontrib>Huang, Chuangxia</creatorcontrib><creatorcontrib>Niezabitowski, Michal</creatorcontrib><creatorcontrib>Bagdasar, Ovidiu</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pratap, Anbalagan</au><au>Raja, Ramachandran</au><au>Cao, Jinde</au><au>Huang, Chuangxia</au><au>Niezabitowski, Michal</au><au>Bagdasar, Ovidiu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2021-01-15</date><risdate>2021</risdate><volume>44</volume><issue>1</issue><spage>419</spage><epage>440</epage><pages>419-440</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete‐time fractional‐order complex‐valued neural networks with time delays. When the fractional‐order β holds 1 < β < 2, sufficient criteria based on a discrete version of generalized Gronwall inequality and rising function property are established for ensuring the finite stability of addressing fractional‐order discrete‐time‐delayed complex‐valued neural networks (FODCVNNs). In the meanwhile, when the fractional‐order β holds 0 < β < 1, a global Mittag–Leffler stability criterion of a class of FODCVNNs is demonstrated with two classes of neuron activation function by means of two different new inequalities, fractional‐order discrete‐time Lyapunov method, discrete version Laplace transforms as well as a discrete version of Mittag–Leffler function. Finally, computer simulations of two numerical examples are illustrated to the correctness and effectiveness of the presented stability results.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.6745</doi><tpages>22</tpages><orcidid>https://orcid.org/0000-0002-0732-226X</orcidid><orcidid>https://orcid.org/0000-0003-4553-5351</orcidid><orcidid>https://orcid.org/0000-0003-3133-7119</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0170-4214 |
| ispartof | Mathematical methods in the applied sciences, 2021-01, Vol.44 (1), p.419-440 |
| issn | 0170-4214 1099-1476 |
| language | eng |
| recordid | cdi_proquest_journals_2465901374 |
| source | Wiley Online Library Journals Frontfile Complete |
| subjects | complex‐valued neural networks discrete time finite‐time stability fractional‐order Laplace transforms Mittag–Leffler stability Neural networks Stability criteria |
| title | Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-10T04%3A23%3A21IST&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=Stability%20of%20discrete%E2%80%90time%20fractional%E2%80%90order%20time%E2%80%90delayed%20neural%20networks%20in%20complex%20field&rft.jtitle=Mathematical%20methods%20in%20the%20applied%20sciences&rft.au=Pratap,%20Anbalagan&rft.date=2021-01-15&rft.volume=44&rft.issue=1&rft.spage=419&rft.epage=440&rft.pages=419-440&rft.issn=0170-4214&rft.eissn=1099-1476&rft_id=info:doi/10.1002/mma.6745&rft_dat=%3Cproquest_cross%3E2465901374%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=2465901374&rft_id=info:pmid/&rfr_iscdi=true |