IMECC UNICAMP, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083970 Campinas, SP - Brazil
 UFMT Sinop, Inst Ciencia Nat Humanas & Sociais, Setor Ind, Av Alexandre Ferronato 1-200, BR-78557267 Sinop, MT - Brazil
 Escuela Tecn Super Ingn, Dept Matemat Aplicada, Avda Descubrimientos, Seville 41092 - Spain
Total Affiliations: 3
PHYSICA D-NONLINEAR PHENOMENA;
JUN 15 2016.
Web of Science Citations:
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)