{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:38:22Z","timestamp":1753882702277,"version":"3.41.2"},"reference-count":190,"publisher":"World Scientific Pub Co Pte Ltd","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,11]]},"abstract":"<jats:p>Symmetries in the external world constrain the evolution of neuronal circuits that allow organisms to sense the environment and act within it. Many small \u201cmodular\u201d circuits can be viewed as approximate discretizations of the relevant symmetries, relating their forms to the functions they perform. The recent development of a formal theory of dynamics and bifurcations of networks of coupled differential equations permits the analysis of some aspects of network behavior without invoking specific model equations or numerical simulations. We review basic features of this theory, compare it to equivariant dynamics, and examine the subtle effects of symmetry when combined with network structure. We illustrate the relation between form and function through examples drawn from neurobiology, including locomotion, peristalsis, visual perception, balance, hearing, location detection, decision-making, and the connectome of the nematode Caenorhabditis elegans.<\/jats:p>","DOI":"10.1142\/s0218127422300336","type":"journal-article","created":{"date-parts":[[2022,12,2]],"date-time":"2022-12-02T06:09:32Z","timestamp":1669961372000},"source":"Crossref","is-referenced-by-count":0,"title":["Symmetry and Network Topology in Neuronal Circuits: Complicity of Form and Function"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3759-0142","authenticated-orcid":false,"given":"Ian","family":"Stewart","sequence":"first","affiliation":[{"name":"Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2022,11,29]]},"reference":[{"key":"S0218127422300336BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408020367"},{"key":"S0218127422300336BIB002","unstructured":"Altun, Z. F., Herndon, L. A., Wolkow, C. A., Crocker, C., Lints, R. & Hall, D. H. [2002] (eds.) WormAtlas 2002\u20132019, http:\/\/www.wormatlas.org."},{"key":"S0218127422300336BIB003","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1145\/800141.804655","volume-title":"Proc. Twelfth Annual ACM Symposium on Theory of Computing","author":"Angluin D.","year":"1980"},{"key":"S0218127422300336BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015167"},{"key":"S0218127422300336BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407017641"},{"key":"S0218127422300336BIB006","doi-asserted-by":"publisher","DOI":"10.1063\/1.3563581"},{"journal-title":"IEEE Trans. Automatic Control","year":"2022","author":"Bizyaeva A.","key":"S0218127422300336BIB007"},{"key":"S0218127422300336BIB008","doi-asserted-by":"crossref","first-page":"3139","DOI":"10.1523\/JNEUROSCI.12-08-03139.1992","volume":"12","author":"Blasdel G. G.","year":"1992","journal-title":"J. Neurosci."},{"key":"S0218127422300336BIB009","first-page":"478","volume":"40","author":"Bock W. J.","year":"2000","journal-title":"Am. Zool."},{"key":"S0218127422300336BIB010","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0012-365X(00)00455-6","volume":"243","author":"Boldi P.","year":"2002","journal-title":"Discr. Math."},{"key":"S0218127422300336BIB011","doi-asserted-by":"crossref","DOI":"10.3389\/fncom.2012.00010","volume":"6","author":"Boyle J. H.","year":"2012","journal-title":"Front. Comput. Neurosci."},{"key":"S0218127422300336BIB012","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1037\/h0075805","volume":"16","author":"Breese B. B.","year":"2009","journal-title":"Psychol. Rev."},{"key":"S0218127422300336BIB013","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1098\/rstb.2000.0769","volume":"356","author":"Bressloff P. C.","year":"2001","journal-title":"Phil. Trans. R. Soc. Lond. B"},{"key":"S0218127422300336BIB014","doi-asserted-by":"crossref","first-page":"078102","DOI":"10.1103\/PhysRevLett.88.078102","volume":"88","author":"Bressloff P. C.","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"S0218127422300336BIB015","doi-asserted-by":"publisher","DOI":"10.1162\/089976602317250861"},{"key":"S0218127422300336BIB016","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.1098\/rstb.2002.1109","volume":"358","author":"Bressloff P. C.","year":"2003","journal-title":"Phil. Trans. R. Soc. Lond. B"},{"key":"S0218127422300336BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s002850000073"},{"key":"S0218127422300336BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/s002850000058"},{"key":"S0218127422300336BIB020","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.physd.2003.08.003","volume":"188","author":"Buono P.-L.","year":"2004","journal-title":"Physica D"},{"key":"S0218127422300336BIB021","series-title":"Symp. Soc. Exp. Biol.","first-page":"195","volume-title":"Neural Origin of Rhythmic Movements","volume":"37","author":"Calabrese R.","year":"1983"},{"key":"S0218127422300336BIB022","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1038\/313477a0","volume":"313","author":"Calford M. B.","year":"1985","journal-title":"Nature"},{"key":"S0218127422300336BIB023","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.1109\/IECON.2010.5675454","volume-title":"IECON 2010 \u2014 36th Annual Conference on IEEE Industrial Electronics Society","author":"Campos R.","year":"2010"},{"key":"S0218127422300336BIB024","first-page":"75","volume-title":"Proc. Austral. Physiol. Soc.","volume":"44","author":"Chambers J. D.","year":"2013"},{"key":"S0218127422300336BIB025","first-page":"18968","volume-title":"Proc. Natl. Acad. Sci. USA","volume":"109","author":"Chechik G.","year":"2012"},{"key":"S0218127422300336BIB026","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1007\/BF02777979","volume":"31","author":"Cicogna G.","year":"1981","journal-title":"Lett. Nuovo Cimento"},{"key":"S0218127422300336BIB027","doi-asserted-by":"crossref","first-page":"2504","DOI":"10.1109\/IJCNN.1993.714233","volume-title":"Proc. 1993 Int. Conf. Neural Networks (IJCNN-93-Nagoya, Japan)","volume":"3","author":"Clippingdale S.","year":"1993"},{"key":"S0218127422300336BIB028","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1016\/0893-6080(95)00077-1","volume":"9","author":"Clippingdale S.","year":"1996","journal-title":"Neural Netw."},{"key":"S0218127422300336BIB029","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1016\/0166-2236(92)90006-T","volume":"15","author":"Cohen A. H.","year":"1992","journal-title":"Trends Neurosci."},{"key":"S0218127422300336BIB030","doi-asserted-by":"publisher","DOI":"10.1007\/BF00201854"},{"key":"S0218127422300336BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/BF02429870"},{"volume-title":"The Collapse of Chaos","year":"1994","author":"Cohen J.","key":"S0218127422300336BIB032"},{"key":"S0218127422300336BIB033","first-page":"1","volume-title":"Nonlinear Phenomena in Biological and Physical Sciences","author":"Cohen J.","year":"2000"},{"key":"S0218127422300336BIB034","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2009.12.010"},{"key":"S0218127422300336BIB035","first-page":"321","volume-title":"Proc. Roy. Soc. Edinburgh","volume":"85","author":"Dancer E. N.","year":"1980"},{"volume-title":"Systems of Nonlinear Partial Differential Equations","year":"1983","author":"Dancer E. N.","key":"S0218127422300336BIB036"},{"volume-title":"Introduction to Lattices and Order","year":"1990","author":"Davey B. A.","key":"S0218127422300336BIB037"},{"key":"S0218127422300336BIB038","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1038\/364620a0","volume":"364","author":"Dear S. P.","year":"1993","journal-title":"Nature"},{"key":"S0218127422300336BIB039","doi-asserted-by":"publisher","DOI":"10.1142\/S0219525900000078"},{"key":"S0218127422300336BIB040","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1080\/01621459.1974.10480137","volume":"69","author":"DeGroot M. H.","year":"1974","journal-title":"J. Amer. Statist. Assoc."},{"volume-title":"Spatial Vision","year":"1988","author":"De Valois R. L.","key":"S0218127422300336BIB041"},{"key":"S0218127422300336BIB042","volume":"17","author":"DeVille L.","year":"2013","journal-title":"J. Eur. Math. Soc."},{"key":"S0218127422300336BIB043","first-page":"2015","volume":"11","author":"DeVille L.","year":"2015","journal-title":"SIGMA"},{"key":"S0218127422300336BIB044","doi-asserted-by":"publisher","DOI":"10.1137\/110858392"},{"key":"S0218127422300336BIB045","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1186\/2190-8567-3-6","volume":"3","author":"Diekman C.","year":"2013","journal-title":"J. Math. Neuro."},{"key":"S0218127422300336BIB046","volume":"4","author":"Diekman C.","year":"2014","journal-title":"J. Math. Neuro."},{"key":"S0218127422300336BIB048","doi-asserted-by":"crossref","first-page":"920","DOI":"10.1038\/35104092","volume":"2","author":"Eagleman D. M.","year":"2001","journal-title":"Nat. Rev.: Neurosci."},{"key":"S0218127422300336BIB049","doi-asserted-by":"publisher","DOI":"10.1038\/35002125"},{"key":"S0218127422300336BIB050","doi-asserted-by":"publisher","DOI":"10.1007\/BF00336965"},{"key":"S0218127422300336BIB051","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87708-2"},{"key":"S0218127422300336BIB052","series-title":"Elements of Psychophysics","volume-title":"Elemente der Psychophysik","author":"Fechner G. T.","year":"1860"},{"key":"S0218127422300336BIB053","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1038\/363449a0","volume":"363","author":"Ffrench-Constant R. H.","year":"1993","journal-title":"Nature"},{"key":"S0218127422300336BIB054","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1080\/14689360410001729379","volume":"19","author":"Field M.","year":"2004","journal-title":"Dyn. Syst."},{"key":"S0218127422300336BIB055","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(61)86902-6"},{"journal-title":"SIADS.","year":"2022","author":"Franci A.","key":"S0218127422300336BIB056"},{"key":"S0218127422300336BIB057","first-page":"1","volume-title":"Advances in Group Processes","volume":"16","author":"Friedkin N. E.","year":"1999"},{"volume-title":"The Enteric Nervous System","year":"2008","author":"Furness J. B.","key":"S0218127422300336BIB058"},{"volume-title":"How Mammals Run: Anatomical Adaptations","year":"1974","author":"Gambaryan P.","key":"S0218127422300336BIB059"},{"key":"S0218127422300336BIB060","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-021-04268-7"},{"key":"S0218127422300336BIB061","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1016\/j.cell.2011.08.051","volume":"147","author":"Giocomo L. M.","year":"2011","journal-title":"Cell"},{"key":"S0218127422300336BIB062","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2013.00024"},{"key":"S0218127422300336BIB063","series-title":"Neuro-Informatics and Neural Modelling","first-page":"887","volume-title":"Handbook of Biological Physics","volume":"4","author":"Golomb D.","year":"2001"},{"key":"S0218127422300336BIB064","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.4249\/scholarpedia.1347","volume":"2","author":"Golomb D.","year":"2007","journal-title":"Scholarpedia"},{"key":"S0218127422300336BIB065","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(81)90045-0"},{"key":"S0218127422300336BIB066","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5034-0"},{"key":"S0218127422300336BIB067","doi-asserted-by":"publisher","DOI":"10.1007\/BF00280698"},{"key":"S0218127422300336BIB068","series-title":"Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, July 1985, Arcata, Contemporary Math.","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1090\/conm\/056\/855088","volume-title":"Multiparameter Bifurcation Theory","volume":"56","author":"Golubitsky M.","year":"1986"},{"key":"S0218127422300336BIB069","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4574-2"},{"key":"S0218127422300336BIB070","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(97)00222-4"},{"key":"S0218127422300336BIB071","doi-asserted-by":"publisher","DOI":"10.1038\/44416"},{"key":"S0218127422300336BIB072","first-page":"277","volume-title":"Global Analysis of Dynamical Systems: Festschrift Dedicated to Floris Takens on the Occasion of his 60th Birthday","author":"Golubitsky M.","year":"2001"},{"key":"S0218127422300336BIB073","series-title":"Progress in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8167-8","volume-title":"The Symmetry Perspective: From Equilibria to Chaos in Phase Space and Physical Space","volume":"200","author":"Golubitsky M.","year":"2002"},{"key":"S0218127422300336BIB074","doi-asserted-by":"publisher","DOI":"10.1137\/040612634"},{"key":"S0218127422300336BIB075","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-06-01108-6"},{"key":"S0218127422300336BIB076","doi-asserted-by":"publisher","DOI":"10.1137\/060667773"},{"key":"S0218127422300336BIB077","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/23\/12\/012"},{"key":"S0218127422300336BIB078","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/25\/4\/1045"},{"key":"S0218127422300336BIB079","doi-asserted-by":"publisher","DOI":"10.1152\/jn.00438.2019"},{"volume-title":"Dynamics and Bifurcation in Networks","year":"2023","author":"Golubitsky M.","key":"S0218127422300336BIB080"},{"key":"S0218127422300336BIB081","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1641\/0006-3568(2003)053[0965:WDFCTU]2.0.CO;2","volume":"53","author":"Grant R. B.","year":"2003","journal-title":"BioScience"},{"key":"S0218127422300336BIB082","doi-asserted-by":"crossref","first-page":"e0182461","DOI":"10.1371\/journal.pone.0182461","volume":"12","author":"Greiter W.","year":"2017","journal-title":"PLoS ONE"},{"key":"S0218127422300336BIB083","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1146\/annurev.ne.08.030185.001313","volume":"8","author":"Grillner S.","year":"1985","journal-title":"Ann. Rev. Neurosci."},{"key":"S0218127422300336BIB084","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1749-6632.1998.tb09035.x","volume":"860","author":"Grillner S.","year":"1998","journal-title":"Ann. NY Acad. Sci."},{"key":"S0218127422300336BIB085","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.asd.2009.10.008","volume":"39","author":"Grimaldi D. A.","year":"2010","journal-title":"Arthropod. Struct. Develop."},{"key":"S0218127422300336BIB086","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"S0218127422300336BIB087","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1038\/nature03721","volume":"436","author":"Hafting T.","year":"2005","journal-title":"Nature"},{"key":"S0218127422300336BIB088","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1523\/JNEUROSCI.11-01-00001.1991","volume":"11","author":"Hall D. H.","year":"1991","journal-title":"J. Neurosci."},{"volume-title":"Infinite-Dimensional Dynamical Systems","year":"1993","author":"Hale J. K.","key":"S0218127422300336BIB089"},{"key":"S0218127422300336BIB090","series-title":"London Math. Soc. Lecture Notes","volume-title":"Theory and Applications of Hopf Bifurcation","volume":"41","author":"Hassard B. D.","year":"1981"},{"volume-title":"The Organization of Behavior","year":"1949","author":"Hebb D. O.","key":"S0218127422300336BIB091"},{"key":"S0218127422300336BIB092","first-page":"121","volume":"5","author":"Hegselmann R.","year":"2002","journal-title":"J. Artif. Soc. Social Simulat."},{"key":"S0218127422300336BIB093","series-title":"Van Nostrand Reinhold Mathematical Studies","volume-title":"Notes on Categories and Groupoids","volume":"32","author":"Higgins P. J.","year":"1971"},{"key":"S0218127422300336BIB094","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1037\/h0070888","volume":"24","author":"Hotelling H.","year":"1993","journal-title":"J. Educat. Psychol."},{"key":"S0218127422300336BIB095","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1113\/jphysiol.1962.sp006837","volume":"160","author":"Hubel D. H.","year":"1962","journal-title":"J. Physiol. (Lond.)"},{"key":"S0218127422300336BIB096","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1038\/nature23019","volume":"547","author":"Iacaruso M. F.","year":"2017","journal-title":"Nature"},{"key":"S0218127422300336BIB097","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0167-2789(84)90268-9","volume":"12","author":"Ihrig E.","year":"1984","journal-title":"Physica D"},{"key":"S0218127422300336BIB098","first-page":"2230001-1","volume":"32","author":"In V.","year":"2022","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127422300336BIB099","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0997-3"},{"volume-title":"Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting","year":"2007","author":"Izhikevich E. M.","key":"S0218127422300336BIB100"},{"journal-title":"Phil. Trans. R. Soc. Lond. B","year":"2018","author":"Izquierdo E. J.","key":"S0218127422300336BIB101"},{"key":"S0218127422300336BIB102","first-page":"299","volume":"54","author":"Jastrow J.","year":"1899","journal-title":"Popular Science Monthly"},{"key":"S0218127422300336BIB103","series-title":"Springer Series in Statistics","volume-title":"Principal Component Analysis","author":"Jolliffe I. T.","year":"2002"},{"key":"S0218127422300336BIB104","doi-asserted-by":"publisher","DOI":"10.1137\/100819795"},{"key":"S0218127422300336BIB105","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195121049.001.0001","volume-title":"Investigations","author":"Kauffman S.","year":"2000"},{"volume-title":"Reinventing the Sacred","year":"2008","author":"Kauffman S.","key":"S0218127422300336BIB106"},{"volume-title":"Mescal and Mechanisms of Hallucinations","year":"1966","author":"Kl\u00fcver H.","key":"S0218127422300336BIB107"},{"volume-title":"Self-Organization and Associative Memory","year":"1984","author":"Kohonen T.","key":"S0218127422300336BIB108"},{"key":"S0218127422300336BIB109","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160390504"},{"volume-title":"Neural Control of Rhythmic Movements in Vertebrates","year":"1988","author":"Kopell N.","key":"S0218127422300336BIB110"},{"key":"S0218127422300336BIB111","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(88)90059-4"},{"key":"S0218127422300336BIB112","doi-asserted-by":"publisher","DOI":"10.1137\/0150062"},{"key":"S0218127422300336BIB113","first-page":"10586","volume-title":"Proc. Natl. Acad. Sci. USA","volume":"91","author":"Kopell N.","year":"1994"},{"key":"S0218127422300336BIB114","first-page":"15508","volume-title":"Proc. Natl. Acad. Sci. USA","volume":"93","author":"Kov\u00e1cs I.","year":"1996"},{"key":"S0218127422300336BIB115","doi-asserted-by":"crossref","first-page":"2327","DOI":"10.1139\/z87-352","volume":"65","author":"Kukalov\u00e1-Peck J.","year":"1987","journal-title":"Canad. J. Zool."},{"key":"S0218127422300336BIB116","first-page":"457","volume":"2","author":"Kupka I.","year":"1963","journal-title":"Contrib. Diff. Eqs."},{"key":"S0218127422300336BIB117","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69689-3"},{"journal-title":"PLOS Comput. Biol.","year":"2020","author":"Leifer I.","key":"S0218127422300336BIB118"},{"key":"S0218127422300336BIB119","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(82)90042-9"},{"key":"S0218127422300336BIB120","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/19\/10\/004"},{"key":"S0218127422300336BIB121","doi-asserted-by":"publisher","DOI":"10.1016\/S1364-6613(99)01332-7"},{"key":"S0218127422300336BIB122","first-page":"3677","volume-title":"IEEE Chinese Control and Decision Conf.","author":"Liu C.","year":"2009"},{"key":"S0218127422300336BIB123","doi-asserted-by":"crossref","first-page":"1728","DOI":"10.1126\/science.1105458","volume":"307","author":"MacFadden B. J.","year":"2005","journal-title":"Science"},{"key":"S0218127422300336BIB124","series-title":"Understanding Complex Systems Series","volume-title":"Symmetries of Living Systems: Graph Fibrations and Cluster Synchronization in Biological Networks","author":"Makse H.","year":"2021"},{"key":"S0218127422300336BIB125","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s00422-003-0461-3","volume":"90","author":"McCollum G.","year":"2004","journal-title":"Biol. Cybern."},{"key":"S0218127422300336BIB126","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(68)90007-2"},{"key":"S0218127422300336BIB127","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/0141-5425(93)90008-M","volume":"15","author":"Miftakhov R. N.","year":"1993","journal-title":"J. Biomed. Eng."},{"key":"S0218127422300336BIB128","doi-asserted-by":"publisher","DOI":"10.1016\/1350-4533(95)90372-I"},{"key":"S0218127422300336BIB129","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1006\/jtbi.1998.0859","volume":"197","author":"Miftakhov R. N.","year":"1999","journal-title":"J. Theort. Biol."},{"key":"S0218127422300336BIB130","doi-asserted-by":"crossref","first-page":"4961","DOI":"10.1038\/s41467-019-12675-8","volume":"10","author":"Morone F.","year":"2019","journal-title":"Nature Commun."},{"key":"S0218127422300336BIB131","first-page":"8306","volume-title":"Proc. Natl. Acad. Sci.","volume":"117","author":"Morone F.","year":"2020"},{"key":"S0218127422300336BIB132","doi-asserted-by":"publisher","DOI":"10.1038\/nrn3766"},{"key":"S0218127422300336BIB133","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-08539-4"},{"key":"S0218127422300336BIB135","first-page":"2061","volume-title":"Proc. IRE","volume":"50","author":"Nagumo J. S.","year":"1962"},{"key":"S0218127422300336BIB136","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/14786443208647909","volume":"1","author":"Necker L. A.","year":"1832","journal-title":"London and Edinburgh Philos. Mag. J. Sci."},{"key":"S0218127422300336BIB137","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534525.001.0001","volume-title":"Groups and Geometry","author":"Neumann P. M.","year":"1994"},{"key":"S0218127422300336BIB138","doi-asserted-by":"crossref","first-page":"863","DOI":"10.4171\/ggd\/111","volume":"4","author":"Neumann W. D.","year":"2011","journal-title":"Groups Geom. Dyn."},{"key":"S0218127422300336BIB139","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.110.174102","volume":"110","author":"Nicosia V.","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"S0218127422300336BIB140","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0166-218X(93)E0133-J","volume":"56","author":"Norris N.","year":"1995","journal-title":"Discr. Appl. Math."},{"journal-title":"Front. Comput. Neurosci.","year":"2021","author":"Olivares E.","key":"S0218127422300336BIB141"},{"key":"S0218127422300336BIB142","doi-asserted-by":"crossref","first-page":"4958","DOI":"10.1523\/JNEUROSCI.16-16-04958.1996","volume":"16","author":"Olsen O. H.","year":"1996","journal-title":"J. Neurosci."},{"key":"S0218127422300336BIB143","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4350-2"},{"key":"S0218127422300336BIB144","first-page":"1","volume":"6","author":"Osterberg G. A.","year":"1935","journal-title":"Acta Ophthalmologica"},{"volume-title":"Rock Art Symbols of the Greater Southwest","year":"1992","author":"Patterson A.","key":"S0218127422300336BIB145"},{"key":"S0218127422300336BIB146","doi-asserted-by":"publisher","DOI":"10.1080\/14786440109462720"},{"key":"S0218127422300336BIB147","volume":"5","author":"Pecora L. M.","year":"2013","journal-title":"Nature Commun."},{"key":"S0218127422300336BIB148","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/0022-0396(67)90026-5","volume":"3","author":"Peixoto M. M.","year":"1966","journal-title":"J. Diff. Eqs."},{"key":"S0218127422300336BIB149","doi-asserted-by":"crossref","DOI":"10.1016\/j.neuron.2017.05.013","volume":"94","author":"Pillai A. S.","year":"2017","journal-title":"Neuron"},{"key":"S0218127422300336BIB150","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-006-0021-2"},{"journal-title":"Front. Comput. Neurosci.","year":"2021","author":"Pizlo Z.","key":"S0218127422300336BIB151"},{"key":"S0218127422300336BIB152","doi-asserted-by":"publisher","DOI":"10.1063\/1.2959145"},{"key":"S0218127422300336BIB153","series-title":"Surveys and Reference Works in Math.","volume-title":"Catastrophe Theory and Its Applications","volume":"2","author":"Poston T.","year":"1978"},{"key":"S0218127422300336BIB154","doi-asserted-by":"crossref","first-page":"1503","DOI":"10.1098\/rsif.2010.0183","volume":"7","author":"Purcell O.","year":"2010","journal-title":"J. R. Soc. Interface"},{"key":"S0218127422300336BIB156","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1038\/s41586-020-2894-4","volume":"588","author":"Rossi L. F.","year":"2020","journal-title":"Nature"},{"key":"S0218127422300336BIB157","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1162\/neco_a_01150","volume":"31","author":"Ryabakken E.","year":"2019","journal-title":"Neural Comput."},{"key":"S0218127422300336BIB158","first-page":"13737","volume":"11","author":"Sakamoto K.","year":"2021","journal-title":"Nat. Sci. Rep."},{"key":"S0218127422300336BIB159","first-page":"81","volume-title":"Hallucinations: Behavior, Experience and Theory","author":"Siegel R. K.","year":"1975"},{"volume-title":"Horses","year":"1951","author":"Simpson G. G.","key":"S0218127422300336BIB160"},{"key":"S0218127422300336BIB161","doi-asserted-by":"publisher","DOI":"10.1016\/S0896-6273(00)80821-1"},{"key":"S0218127422300336BIB162","doi-asserted-by":"crossref","first-page":"22074","DOI":"10.1038\/srep22074","volume":"6","author":"Singh R.","year":"2016","journal-title":"Sci. Rep."},{"key":"S0218127422300336BIB163","first-page":"97","volume":"17","author":"Smale S.","year":"1963","journal-title":"Ann. Scuola Normale Superiore Pisa"},{"key":"S0218127422300336BIB164","doi-asserted-by":"publisher","DOI":"10.1152\/ajpcell.1998.274.2.C531"},{"key":"S0218127422300336BIB165","doi-asserted-by":"crossref","first-page":"e1000028","DOI":"10.1371\/journal.pcbi.1000028","volume":"4","author":"Stephens G. J.","year":"2008","journal-title":"PLoS Comput. Biol."},{"key":"S0218127422300336BIB166","doi-asserted-by":"publisher","DOI":"10.1137\/1035134"},{"key":"S0218127422300336BIB167","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7982-8_1"},{"key":"S0218127422300336BIB168","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111103419896"},{"key":"S0218127422300336BIB169","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004107000345"},{"key":"S0218127422300336BIB170","doi-asserted-by":"publisher","DOI":"10.1080\/14689360701450410"},{"key":"S0218127422300336BIB171","doi-asserted-by":"publisher","DOI":"10.1080\/14689360701631126"},{"key":"S0218127422300336BIB172","doi-asserted-by":"publisher","DOI":"10.3390\/sym6010023"},{"key":"S0218127422300336BIB173","doi-asserted-by":"crossref","first-page":"1730049-1","DOI":"10.1142\/S021812741730049X","volume":"27","author":"Stewart I.","year":"2017","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127422300336BIB174","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741930026X"},{"key":"S0218127422300336BIB175","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127420300049"},{"key":"S0218127422300336BIB176","doi-asserted-by":"crossref","first-page":"799","DOI":"10.3390\/sym11060799","volume":"11","author":"Stewart I.","year":"2020","journal-title":"Symmetry"},{"key":"S0218127422300336BIB177","first-page":"2050212-1","volume":"30","author":"Stewart I.","year":"2020","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"S0218127422300336BIB178","doi-asserted-by":"publisher","DOI":"10.4171\/PM\/2048"},{"key":"S0218127422300336BIB179","doi-asserted-by":"crossref","first-page":"2130019-1","DOI":"10.1142\/S0218127421300196","volume":"31","author":"Stewart I.","year":"2021","journal-title":"Int. J. Bifurcation and Chaos"},{"journal-title":"Portugaliae Mathematica","year":"2022","author":"Stewart I.","key":"S0218127422300336BIB180"},{"key":"S0218127422300336BIB183","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1016\/S0960-9822(02)00592-4","volume":"6","author":"Swindale N. V.","year":"1996","journal-title":"Current Biol."},{"key":"S0218127422300336BIB184","first-page":"81","volume-title":"Proc. R. Soc. Lond. B","volume":"261","author":"Tanaka S.","year":"1985"},{"key":"S0218127422300336BIB185","doi-asserted-by":"publisher","DOI":"10.1016\/j.tics.2006.09.003"},{"volume-title":"Front. Integr. Neurosci.","year":"2009","author":"Uhlhaas P. J.","key":"S0218127422300336BIB186"},{"key":"S0218127422300336BIB187","first-page":"862","volume-title":"Proc. Natl. Acad. Sci.","volume":"113","author":"Van Valkenburgh B.","year":"2016"},{"key":"S0218127422300336BIB189","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1001066"},{"key":"S0218127422300336BIB190","doi-asserted-by":"crossref","first-page":"e08362","DOI":"10.7554\/eLife.08362","volume":"4","author":"Wei X.-X.","year":"2015","journal-title":"eLife"},{"key":"S0218127422300336BIB191","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.1986.0056"},{"key":"S0218127422300336BIB193","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/s00422-017-0721-2","volume":"111","author":"Wilshin S.","year":"2017","journal-title":"Biol. Cybernet."},{"key":"S0218127422300336BIB194","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(72)86068-5"},{"key":"S0218127422300336BIB195","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1016\/0893-6080(95)00077-1","volume":"9","author":"Wilson R.","year":"1996","journal-title":"Neural Networks"},{"key":"S0218127422300336BIB196","first-page":"14499","volume-title":"Proc. Natl. Acad. Sci.","volume":"100","author":"Wilson H. R.","year":"2003"},{"key":"S0218127422300336BIB197","doi-asserted-by":"publisher","DOI":"10.1016\/j.visres.2007.07.007"},{"key":"S0218127422300336BIB198","first-page":"399","volume-title":"Cortical Mechanisms of Vision","author":"Wilson H. R.","year":"2009"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127422300336","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,2]],"date-time":"2023-12-02T09:18:25Z","timestamp":1701508705000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218127422300336"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11]]},"references-count":190,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["10.1142\/S0218127422300336"],"URL":"https:\/\/doi.org\/10.1142\/s0218127422300336","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2022,11]]},"article-number":"2230033"}}