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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones

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Author(s):
Euzebio, Rodrigo [1] ; Pazim, Rubens [2] ; Ponce, Enrique [3]
Total Authors: 3
Affiliation:
[1] IMECC UNICAMP, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083970 Campinas, SP - Brazil
[2] UFMT Sinop, Inst Ciencia Nat Humanas & Sociais, Setor Ind, Av Alexandre Ferronato 1-200, BR-78557267 Sinop, MT - Brazil
[3] Escuela Tecn Super Ingn, Dept Matemat Aplicada, Avda Descubrimientos, Seville 41092 - Spain
Total Affiliations: 3
Document type: Journal article
Source: PHYSICA D-NONLINEAR PHENOMENA; v. 325, p. 74-85, JUN 15 2016.
Web of Science Citations: 3
Abstract

We consider continuous piecewise-linear differential systems with three zones where the central one is degenerate, that is, the determinant of its linear part vanishes. By moving one parameter which is associated to the equilibrium position, we detect some new bifurcations exhibiting jump transitions both in the equilibrium location and in the appearance of limit cycles. In particular, we introduce the scabbard bifurcation, characterized by the birth of a limit cycle from a continuum of equilibrium points. Some of the studied bifurcations are detected, after an appropriate choice of parameters, in a piecewise linear Morris-Lecar model for the activity of a single neuron activity, which is usually considered as a reduction of the celebrated Hodgkin-Huxley equations. (C) 2016 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 14/18508-3 - Minimal sets of piecewise differential systems in dimension 3
Grantee:Rodrigo Donizete Euzébio
Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
FAPESP's process: 13/25828-1 - Minimal sets and invariant manifolds in piecewise smooth systems
Grantee:Rodrigo Donizete Euzébio
Support Opportunities: Scholarships in Brazil - Post-Doctorate