{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T13:06:06Z","timestamp":1760015166149,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T00:00:00Z","timestamp":1661385600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T00:00:00Z","timestamp":1661385600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100013066","name":"Key Scientific Research Project of Colleges and Universities in Henan Province","doi-asserted-by":"publisher","award":["20A110004"],"award-info":[{"award-number":["20A110004"]}],"id":[{"id":"10.13039\/501100013066","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cogn Comput"],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s12559-022-10045-z","type":"journal-article","created":{"date-parts":[[2022,8,25]],"date-time":"2022-08-25T06:03:36Z","timestamp":1661407416000},"page":"466-485","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Dynamical Bifurcations in a Fractional-Order Neural Network with Nonidentical Communication Delays"],"prefix":"10.1007","volume":"15","author":[{"given":"Shansong","family":"Mo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7150-8085","authenticated-orcid":false,"given":"Chengdai","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinde","family":"Cao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Alsaedi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,8,25]]},"reference":[{"key":"10045_CR1","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1016\/j.neunet.2018.03.019","volume":"103","author":"SR Kulkarni","year":"2018","unstructured":"Kulkarni SR, Rajendran B. Spiking neural networks for handwritten digit recognition\u2013supervised learning and network optimization. Neural Netw. 2018;103:118\u201327.","journal-title":"Neural Netw"},{"issue":"12","key":"10045_CR2","doi-asserted-by":"publisher","first-page":"4731","DOI":"10.1016\/j.cnsns.2012.03.030","volume":"17","author":"M Sadeghpour","year":"2012","unstructured":"Sadeghpour M, Khodabakhsh M, Salarieh H. Intelligent control of chaos using linear feedback controller and neural network identifier. Commun Nonlinear Sci Numer Simul. 2012;17(12):4731\u20139.","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"3\u20134","key":"10045_CR3","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/0025-5564(72)90075-2","volume":"14","author":"JA Anderson","year":"1972","unstructured":"Anderson JA. A simple neural network generating an interactive memory. Math Biosci. 1972;14(3\u20134):197\u2013220.","journal-title":"Math Biosci"},{"issue":"7","key":"10045_CR4","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1109\/81.401145","volume":"42","author":"M Forti","year":"1995","unstructured":"Forti M, Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans Circuits Syst I Fundam Theory Appl. 1995;42(7):354\u201366.","journal-title":"IEEE Trans Circuits Syst I Fundam Theory Appl"},{"issue":"1","key":"10045_CR5","first-page":"1","volume":"26","author":"S Abbas","year":"2018","unstructured":"Abbas S, Coronel A, Pinto M, Tyagi S. Exponential approximation of solutions of bidirectional neural networks model with positive delay. Neural Parallel Sci Comput. 2018;26(1):1\u201329.","journal-title":"Neural Parallel Sci Comput"},{"key":"10045_CR6","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.neunet.2020.02.008","volume":"125","author":"L Chen","year":"2020","unstructured":"Chen L, Yin H, Huang T, Yuan L, Zheng S, Yin L. Chaos in fractional-order discrete neural networks with application to image encryption. Neural Netw. 2020;125:174\u201384.","journal-title":"Neural Netw"},{"key":"10045_CR7","doi-asserted-by":"crossref","unstructured":"Yang F, Mou J, Liu J, Ma C, Yan H. Characteristic analysis of the fractional-order hyperchaotic complex system and its image encryption application. Signal Process. 2020;169:107373.","DOI":"10.1016\/j.sigpro.2019.107373"},{"issue":"2","key":"10045_CR8","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1115\/1.3167616","volume":"51","author":"R Koeller","year":"1984","unstructured":"Koeller R. Applications of fractional calculus to the theory of viscoelasticity. J Appl Mech. 1984;51(2):299\u2013307.","journal-title":"J Appl Mech"},{"issue":"3","key":"10045_CR9","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1007\/BF00437306","volume":"33","author":"N Heymans","year":"1994","unstructured":"Heymans N, Bauwens J-C. Fractal rheological models and fractional differential equations for viscoelastic behavior. Rheol Acta. 1994;33(3):210\u20139.","journal-title":"Rheol Acta"},{"key":"10045_CR10","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.pbiomolbio.2018.03.002","volume":"140","author":"A Sohail","year":"2018","unstructured":"Sohail A, B\u00e9g O, Li Z, Celik S. Physics of fractional imaging in biomedicine. Prog Biophys Mol Biol. 2018;140:13\u201320.","journal-title":"Prog Biophys Mol Biol"},{"issue":"3","key":"10045_CR11","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1109\/JETCAS.2013.2265797","volume":"3","author":"TJ Freeborn","year":"2013","unstructured":"Freeborn TJ. A survey of fractional-order circuit models for biology and biomedicine. IEEE J Emerging Sel Top Circuits Syst. 2013;3(3):416\u201324.","journal-title":"IEEE J Emerging Sel Top Circuits Syst"},{"issue":"9","key":"10045_CR12","doi-asserted-by":"publisher","first-page":"2903","DOI":"10.1109\/TCSI.2018.2789907","volume":"65","author":"Y Pu","year":"2018","unstructured":"Pu Y, Yuan X, Yu B. Analog circuit implementation of fractional-order memristor: arbitrary-order lattice scaling fracmemristor. IEEE Trans Circuits Syst I Regul Pap. 2018;65(9):2903\u201316.","journal-title":"IEEE Trans Circuits Syst I Regul Pap"},{"issue":"1","key":"10045_CR13","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/BF00206239","volume":"72","author":"TJ Anastasio","year":"1994","unstructured":"Anastasio TJ. The fractional-order dynamics of brainstem vestibulo-oculomotor neurons. Biol Cybern. 1994;72(1):69\u201379.","journal-title":"Biol Cybern"},{"key":"10045_CR14","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/j.physa.2017.04.124","volume":"483","author":"Y Gu","year":"2017","unstructured":"Gu Y, Yu Y, Wang H. Synchronization-based parameter estimation of fractional-order neural networks. Physica A. 2017;483:351\u201361.","journal-title":"Physica A"},{"key":"10045_CR15","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/j.neucom.2019.06.107","volume":"391","author":"L Sanchez","year":"2020","unstructured":"Sanchez L, Otero J, Ansean D, Couso I. Health assessment of LFP automotive batteries using a fractional-order neural network. Neurocomputing. 2020;391:345\u201354.","journal-title":"Neurocomputing"},{"key":"10045_CR16","doi-asserted-by":"crossref","unstructured":"Aslipour Z, Yazdizadeh A. Identification of nonlinear systems using adaptive variable-order fractional neural networks (case study: A windturbine with practical results).\u00a0Eng Appl Artif Intell.\u00a02019;85:462\u2013473.","DOI":"10.1016\/j.engappai.2019.06.025"},{"issue":"5","key":"10045_CR17","doi-asserted-by":"publisher","first-page":"2095","DOI":"10.1002\/mma.4736","volume":"41","author":"HM Srivastava","year":"2018","unstructured":"Srivastava HM, Abbas S, Tyagi S, Lassoued D. Global exponential stability of fractional-order impulsive neural network with time-varying and distributed delay. Math Methods Appl Sci. 2018;41(5):2095\u2013104.","journal-title":"Math Methods Appl Sci"},{"issue":"1\u20132","key":"10045_CR18","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.physleta.2005.10.056","volume":"351","author":"W Yu","year":"2006","unstructured":"Yu W, Cao J. Stability and HOPF bifurcation analysis on a four-neuron BAM neural network with time delays. Phys Lett A. 2006;351(1\u20132):64\u201378.","journal-title":"Phys Lett A"},{"issue":"7","key":"10045_CR19","doi-asserted-by":"publisher","first-page":"3255","DOI":"10.1016\/j.apm.2011.01.025","volume":"35","author":"N Bairagi","year":"2011","unstructured":"Bairagi N, Jana D. On the stability and Hopf bifurcation of a delay-induced predator\u2013prey system with habitat complexity. Appl Math Model. 2011;35(7):3255\u201367.","journal-title":"Appl Math Model"},{"key":"10045_CR20","doi-asserted-by":"publisher","first-page":"528","DOI":"10.1016\/j.cnsns.2018.07.019","volume":"67","author":"B Dubey","year":"2019","unstructured":"Dubey B, Kumar A, Maiti AP. Global stability and HOPF-bifurcation of prey-predator system with two discrete delays including habitat complexity and prey refuge. Commun Nonlinear Sci Numer Simul. 2019;67:528\u201354.","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"10045_CR21","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1103\/PhysRevA.39.347","volume":"39","author":"C Marcrs","year":"1989","unstructured":"Marcrs C, Westervelt R. Stability of analog neural network with delay. Phys Rev A. 1989;39:347\u201359.","journal-title":"Phys. Rev. A"},{"key":"10045_CR22","unstructured":"Wu J. Introduction to neural dynamics and signal transmission delay, de Gruyter.\u00a02011."},{"key":"10045_CR23","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.ijnonlinmec.2014.10.010","volume":"70","author":"F Han","year":"2015","unstructured":"Han F, Wang Z, Du Y, Sun X, Zhang B. Robust synchronization of bursting Hodgkin-Huxley neuronal systems coupled by delayed chemical synapses. Int J Non-Linear Mech. 2015;70:105\u201311.","journal-title":"Int J Non-Linear Mech"},{"issue":"5","key":"10045_CR24","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1007\/s12559-021-09920-y","volume":"13","author":"S Zhou","year":"2021","unstructured":"Zhou S, Xiao M, Wang L, Cheng Z. Bifurcation and oscillations of a multi-ring coupling neural network with discrete delays. Cogn Comput. 2021;13(5):1233\u201345.","journal-title":"Cogn Comput"},{"key":"10045_CR25","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.neunet.2019.05.002","volume":"117","author":"C Huang","year":"2019","unstructured":"Huang C, Nie X, Zhao X, Song Q, Tu Z, Xiao M, Cao J. Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw. 2019;117:67\u201393.","journal-title":"Neural Netw"},{"issue":"1","key":"10045_CR26","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s11063-019-10093-x","volume":"51","author":"D Ding","year":"2020","unstructured":"Ding D, Yao X, Zhang H. Complex projection synchronization of fractional-order complex-valued memristive neural networks with multiple delays. Neural Process Lett. 2020;51(1):325\u201345.","journal-title":"Neural Process Lett"},{"key":"10045_CR27","doi-asserted-by":"crossref","unstructured":"Rihan F, Velmurugan G. Dynamics of fractional-order delay differential model for tumor-immune system. Chaos, Solitons Fractals. 2020;132:109592.","DOI":"10.1016\/j.chaos.2019.109592"},{"issue":"1","key":"10045_CR28","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1007\/s11063-020-10395-5","volume":"53","author":"C Huang","year":"2021","unstructured":"Huang C, Cao J. Bifurcations induced by self-connection delay in high-order fractional neural networks. Neural Process Lett. 2021;53(1):637\u201351.","journal-title":"Neural Process Lett"},{"issue":"03","key":"10045_CR29","doi-asserted-by":"publisher","first-page":"2150073","DOI":"10.1142\/S0218348X21500730","volume":"29","author":"C Huang","year":"2021","unstructured":"Huang C, Liu H, Chen Y, Chen X, Song F. Dynamics of a fractional-order BAM neural network with leakage delay and communication delay. Fractals. 2021;29(03):2150073.","journal-title":"Fractals"},{"key":"10045_CR30","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1016\/j.matcom.2020.11.023","volume":"182","author":"C Xu","year":"2021","unstructured":"Xu C, Liu Z, Liao M, Li P, Xiao Q, Yuan S. Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of HOPF bifurcation. Math Comput Simul. 2021;182:471\u201394.","journal-title":"Math Comput Simul"},{"key":"10045_CR31","doi-asserted-by":"crossref","unstructured":"Li S, Huang C, Yuan S. Hopf bifurcation of a fractional-order double-ring structured neural network model with multiple communication delays. Nonlinear Dyn. 2022;1\u201318.","DOI":"10.1007\/s11071-021-07177-6"},{"issue":"12","key":"10045_CR32","doi-asserted-by":"publisher","first-page":"6748","DOI":"10.1016\/j.amc.2011.12.042","volume":"218","author":"P Bi","year":"2012","unstructured":"Bi P, Hu Z. Hopf bifurcation and stability for a neural network model with mixed delays. Appl Math Comput. 2012;218(12):6748\u201361.","journal-title":"Appl Math Comput"},{"key":"10045_CR33","unstructured":"Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier;\u00a01998."},{"key":"10045_CR34","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.amc.2018.09.027","volume":"343","author":"J Cao","year":"2019","unstructured":"Cao J, Guerrini L, Cheng Z. Stability and HOPF bifurcation of controlled complex networks model with two delays. Appl Math Comput. 2019;343:21\u20139.","journal-title":"Appl Math Comput"},{"issue":"4","key":"10045_CR35","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s11071-006-9094-0","volume":"48","author":"W Deng","year":"2007","unstructured":"Deng W, Li C, L\u00fc J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn. 2007;48(4):409\u201316.","journal-title":"Nonlinear Dyn"}],"container-title":["Cognitive Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12559-022-10045-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12559-022-10045-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12559-022-10045-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T06:51:54Z","timestamp":1682491914000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12559-022-10045-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,25]]},"references-count":35,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["10045"],"URL":"https:\/\/doi.org\/10.1007\/s12559-022-10045-z","relation":{},"ISSN":["1866-9956","1866-9964"],"issn-type":[{"type":"print","value":"1866-9956"},{"type":"electronic","value":"1866-9964"}],"subject":[],"published":{"date-parts":[[2022,8,25]]},"assertion":[{"value":"18 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 July 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 August 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This article does not contain any studies with human participants performed by any of the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Research Involving Human and Animal Participants"}},{"value":"Informed consent was not required as no humans or animals were involved.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed Consent"}},{"value":"Shansong Mo, Chengdai Huang, Jinde Cao and Ahmed Alsaedi declare that they have no conflict of interest.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}