{"id":"https://openalex.org/W2005709721","doi":"https://doi.org/10.1002/(sici)1097-007x(199605/06)24:3<269::aid-cta915>3.0.co;2-l","title":"Equilibrium analysis of non-symmetric CNNs","display_name":"Equilibrium analysis of non-symmetric CNNs","publication_year":1996,"publication_date":"1996-05-01","ids":{"openalex":"https://openalex.org/W2005709721","doi":"https://doi.org/10.1002/(sici)1097-007x(199605/06)24:3<269::aid-cta915>3.0.co;2-l","mag":"2005709721"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-007x(199605/06)24:3<269::aid-cta915>3.0.co;2-l","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-007x(199605/06)24:3<269::aid-cta915>3.0.co;2-l","pdf_url":null,"source":{"id":"https://openalex.org/S92132303","display_name":"International Journal of Circuit Theory and Applications","issn_l":"0098-9886","issn":["0098-9886","1097-007X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Circuit Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057771990","display_name":"Sabri Arik","orcid":"https://orcid.org/0000-0002-4390-5139"},"institutions":[{"id":"https://openalex.org/I28257850","display_name":"London South Bank University","ror":"https://ror.org/02vwnat91","country_code":"GB","type":"education","lineage":["https://openalex.org/I28257850"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Sabri Arik","raw_affiliation_strings":["Centre for Research in Information Engineering, School of Electrical, Electronic and Information Engineering, South Bank University, Borough Road, London SE1 0AA, UK"],"affiliations":[{"raw_affiliation_string":"Centre for Research in Information Engineering, School of Electrical, Electronic and Information Engineering, South Bank University, Borough Road, London SE1 0AA, UK","institution_ids":["https://openalex.org/I28257850"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054083929","display_name":"V. Tav\u015fanoglu","orcid":"https://orcid.org/0000-0001-8590-1518"},"institutions":[{"id":"https://openalex.org/I28257850","display_name":"London South Bank University","ror":"https://ror.org/02vwnat91","country_code":"GB","type":"education","lineage":["https://openalex.org/I28257850"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Vedat Tavsanoglu","raw_affiliation_strings":["Centre for Research in Information Engineering, School of Electrical, Electronic and Information Engineering, South Bank University, Borough Road, London SE1 0AA, UK"],"affiliations":[{"raw_affiliation_string":"Centre for Research in Information Engineering, School of Electrical, Electronic and Information Engineering, South Bank University, Borough Road, London SE1 0AA, UK","institution_ids":["https://openalex.org/I28257850"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057771990"],"corresponding_institution_ids":["https://openalex.org/I28257850"],"apc_list":{"value":3660,"currency":"USD","value_usd":3660},"apc_paid":null,"fwci":4.7844,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.94531463,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","issue":"3","first_page":"269","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9850999712944031,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9537000060081482,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8760180473327637},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.8688929080963135},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5988032817840576},{"id":"https://openalex.org/keywords/cellular-neural-network","display_name":"Cellular neural network","score":0.5423309803009033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5175987482070923},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4884614050388336},{"id":"https://openalex.org/keywords/saturation","display_name":"Saturation (graph theory)","score":0.4797550439834595},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4414491355419159},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4388788938522339},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3658057451248169},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30446261167526245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2783217430114746},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20127373933792114},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18040496110916138},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09376490116119385},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07775247097015381},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07748919725418091},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.07091042399406433}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8760180473327637},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.8688929080963135},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5988032817840576},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.5423309803009033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5175987482070923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4884614050388336},{"id":"https://openalex.org/C9930424","wikidata":"https://www.wikidata.org/wiki/Q7426587","display_name":"Saturation (graph theory)","level":2,"score":0.4797550439834595},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4414491355419159},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4388788938522339},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3658057451248169},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30446261167526245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2783217430114746},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20127373933792114},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18040496110916138},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09376490116119385},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07775247097015381},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07748919725418091},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.07091042399406433},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-007x(199605/06)24:3<269::aid-cta915>3.0.co;2-l","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-007x(199605/06)24:3<269::aid-cta915>3.0.co;2-l","pdf_url":null,"source":{"id":"https://openalex.org/S92132303","display_name":"International Journal of Circuit Theory and Applications","issn_l":"0098-9886","issn":["0098-9886","1097-007X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Circuit Theory and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2134075948","https://openalex.org/W1978738522","https://openalex.org/W2095028518","https://openalex.org/W2136669799","https://openalex.org/W2377228964","https://openalex.org/W2085071341","https://openalex.org/W2361641056","https://openalex.org/W1973113296","https://openalex.org/W2152189682","https://openalex.org/W2347889085"],"abstract_inverted_index":{"Two":[0],"useful":[1],"results":[2],"concerning":[3],"the":[4,21,29,40,47],"equilibrium":[5,26,48],"analysis":[6],"of":[7,23,46],"non-symmetric":[8],"cellular":[9],"neural":[10],"networks":[11],"(CNNs)":[12],"are":[13],"presented.":[14],"First":[15],"a":[16,24],"new":[17],"sufficient":[18],"condition":[19,37],"ensuring":[20],"existence":[22],"stable":[25],"point":[27,49],"in":[28],"total":[30],"saturation":[31],"region":[32],"is":[33,50],"given.":[34],"Then":[35],"another":[36],"which":[38],"guarantees":[39],"uniqueness":[41],"and":[42],"global":[43],"asymptotic":[44],"stability":[45],"obtained.":[51]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}