000102097 001__ 102097
000102097 005__ 20220426091134.0
000102097 0247_ $$2doi$$a10.1063/1.5138919
000102097 0248_ $$2sideral$$a118682
000102097 037__ $$aART-2020-118682
000102097 041__ $$aeng
000102097 100__ $$0(orcid)0000-0002-8089-343X$$aBarrio, Roberto$$uUniversidad de Zaragoza
000102097 245__ $$aHomoclinic organization in the Hindmarsh-Rose model: A three parameter study
000102097 260__ $$c2020
000102097 5060_ $$aAccess copy available to the general public$$fUnrestricted
000102097 5203_ $$aBursting phenomena are found in a wide variety of fast-slow systems. In this article, we consider the Hindmarsh-Rose neuron model, where, as it is known in the literature, there are homoclinic bifurcations involved in the bursting dynamics. However, the global homoclinic structure is far from being fully understood. Working in a three-parameter space, the results of our numerical analysis show a complex atlas of bifurcations, which extends from the singular limit to regions where a fast-slow perspective no longer applies. Based on this information, we propose a global theoretical description. Surfaces of codimension-one homoclinic bifurcations are exponentially close to each other in the fast-slow regime. Remarkably, explained by the specific properties of these surfaces, we show how the Hindmarsh-Rose model exhibits isolas of homoclinic bifurcations when appropriate two-dimensional slices are considered in the three-parameter space. On the other hand, these homoclinic bifurcation surfaces contain curves corresponding to parameter values where additional degeneracies are exhibited. These codimension-two bifurcation curves organize the bifurcations associated with the spike-adding process and they behave like the "spines-of-a-book, " gathering "pages" of bifurcations of periodic orbits. Depending on how the parameter space is explored, homoclinic phenomena may be absent or far away, but their organizing role in the bursting dynamics is beyond doubt, since the involved bifurcations are generated in them. This is shown in the global analysis and in the proposed theoretical scheme.
000102097 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R$$9info:eu-repo/grantAgreement/ES/DGA/LMP124-18$$9info:eu-repo/grantAgreement/ES/MICINN/PGC2018-096026-B-I00
000102097 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000102097 590__ $$a3.642$$b2020
000102097 591__ $$aPHYSICS, MATHEMATICAL$$b4 / 55 = 0.073$$c2020$$dQ1$$eT1
000102097 591__ $$aMATHEMATICS, APPLIED$$b13 / 265 = 0.049$$c2020$$dQ1$$eT1
000102097 592__ $$a0.97$$b2020
000102097 593__ $$aApplied Mathematics$$c2020$$dQ1
000102097 593__ $$aMathematical Physics$$c2020$$dQ1
000102097 593__ $$aStatistical and Nonlinear Physics$$c2020$$dQ1
000102097 593__ $$aPhysics and Astronomy (miscellaneous)$$c2020$$dQ1
000102097 593__ $$aMedicine (miscellaneous)$$c2020$$dQ1
000102097 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000102097 700__ $$aIbáñez, Santiago
000102097 700__ $$aPérez, Lucía
000102097 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000102097 773__ $$g30, 5 (2020), 053132 [20 pp.]$$pChaos$$tCHAOS$$x1054-1500
000102097 8564_ $$s5978825$$uhttps://zaguan.unizar.es/record/102097/files/texto_completo.pdf$$yVersión publicada
000102097 8564_ $$s2651693$$uhttps://zaguan.unizar.es/record/102097/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000102097 909CO $$ooai:zaguan.unizar.es:102097$$particulos$$pdriver
000102097 951__ $$a2022-04-26-08:52:44
000102097 980__ $$aARTICLE