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

Autor(es)

Euzebio, Rodrigo ^[1] ; Pazim, Rubens ^[2] ; Ponce, Enrique ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA D-NONLINEAR PHENOMENA; v. 325, p. 74-85, JUN 15 2016.
• Citações Web of Science: 3

Resumo

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)

• Processo FAPESP: 14/18508-3 - Conjuntos minimais de sistemas suaves por partes em dimensão 3
• Beneficiário: Rodrigo Donizete Euzébio
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 13/25828-1 - Conjuntos minimais e variedades invariantes em sistemas suaves por partes
• Beneficiário: Rodrigo Donizete Euzébio
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado