{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:24:37Z","timestamp":1787239477060,"version":"build-2736575974"},"reference-count":26,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,4]]},"abstract":"<jats:p>A one-dimensional Gaussian map defined by a Gaussian function describes a discrete-time dynamical system. Chaotic behavior can be observed in both Gaussian and logistic maps. This study analyzes the bifurcation structure corresponding to the fixed and periodic points of a coupled system comprising two Gaussian maps. The bifurcation structure of a mutually coupled Gaussian map is more complex than that of a mutually coupled logistic map. In a coupled Gaussian map, it was confirmed that after a stable fixed point or stable periodic points became unstable through the bifurcation, the points were able to recover their stability while the system parameters were changing. Moreover, we investigated a parameter region in which symmetric and asymmetric stable fixed points coexisted. Asymmetric unstable fixed point was generated by the [Formula: see text]-type branching of a symmetric stable fixed point. The stability of the unstable fixed point could be recovered through period-doubling and tangent bifurcations. Furthermore, a homoclinic structure related to the occurrence of chaotic behavior and invariant closed curves caused by two-periodic points was observed. The mutually coupled Gaussian map was merely a two-dimensional dynamical system; however, chaotic itinerancy, known to be a characteristic property associated with high-dimensional dynamical systems, was observed. The bifurcation structure of the mutually coupled Gaussian map clearly elucidates the mechanism of chaotic itinerancy generation in the two-dimensional coupled map. We discussed this mechanism by comparing the bifurcation structures of the Gaussian and logistic maps.<\/jats:p>","DOI":"10.1142\/s0218127418300112","type":"journal-article","created":{"date-parts":[[2018,5,4]],"date-time":"2018-05-04T04:40:47Z","timestamp":1525408847000},"page":"1830011","source":"Crossref","is-referenced-by-count":2,"title":["Chaotic Itinerancy Observed in Mutually Coupled Gaussian Maps"],"prefix":"10.1142","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3200-2129","authenticated-orcid":false,"given":"Mio","family":"Kobayashi","sequence":"first","affiliation":[{"name":"Department of Creative Technology Engineering, National Institute of Technology, Anan College, 265 Aoki Minobayashi, Anan, Tokushima 774-0017, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tetsuya","family":"Yoshinaga","sequence":"additional","affiliation":[{"name":"Graduate School of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2018,5,4]]},"reference":[{"key":"S0218127418300112BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2015.09.003"},{"key":"S0218127418300112BIB002","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.71.016222"},{"key":"S0218127418300112BIB003","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.4052"},{"key":"S0218127418300112BIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.99.058101"},{"key":"S0218127418300112BIB005","doi-asserted-by":"publisher","DOI":"10.1063\/1.452020"},{"key":"S0218127418300112BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2017.06.025"},{"key":"S0218127418300112BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2012.06.009"},{"key":"S0218127418300112BIB008","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.098105"},{"key":"S0218127418300112BIB009","volume-title":"Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields","volume":"42","author":"Guckenheimer J.","year":"2013"},{"key":"S0218127418300112BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2017.06.006"},{"key":"S0218127418300112BIB011","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198507239.001.0001"},{"key":"S0218127418300112BIB012","doi-asserted-by":"publisher","DOI":"10.1143\/PTPS.99.295"},{"key":"S0218127418300112BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(91)90103-G"},{"key":"S0218127418300112BIB014","doi-asserted-by":"publisher","DOI":"10.1063\/1.1607783"},{"key":"S0218127418300112BIB015","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1984.1085495"},{"key":"S0218127418300112BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2016.06.010"},{"key":"S0218127418300112BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2016.07.059"},{"key":"S0218127418300112BIB018","doi-asserted-by":"publisher","DOI":"10.1038\/261459a0"},{"key":"S0218127418300112BIB019","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.026207"},{"key":"S0218127418300112BIB020","first-page":"29","volume":"3","author":"Patidar V.","year":"2006","journal-title":"Electron. 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