Bifurcations Leading to Nonlinear Oscillations in a 3D Piecewise Linear Memristor Oscillator

Autor(es)

Scarabello, Marluce da Cruz ^[1] ; Messias, Marcelo ^[1]

Afiliação do(s) autor(es)

^[1] UNESP Univ Estadual Paulista, Fac Ciencias & Tecnol, Dept Matemat & Computacao, BR-19060900 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 24, n. 1 JAN 2014.
• Citações Web of Science: 12

Resumo

In this paper, we make a bifurcation analysis of a mathematical model for an electric circuit formed by the four fundamental electronic elements: one memristor, one capacitor, one inductor and one resistor. The considered model is given by a discontinuous piecewise linear system of ordinary differential equations, defined on three zones in R-3, determined by vertical bar z vertical bar < 1 (called the central zone) and vertical bar z vertical bar > 1 (the external zones). We show that the z-axis is filled by equilibrium points of the system, and analyze the linear stability of the equilibria in each zone. Due to the existence of this line of equilibria, the phase space R-3 is foliated by invariant planes transversal to the z-axis and parallel to each other, in each zone. In this way, each solution is contained in a three-piece invariant set formed by part of a plane contained in the central zone, which is extended by two half planes in the external zones. We also show that the system may present nonlinear oscillations, given by the existence of infinitely many periodic orbits, each one belonging to one such invariant set and passing by two of the three zones or passing by the three zones. These orbits arise due to homoclinic and heteroclinic bifurcations, obtained varying one parameter in the studied model, and may also exist for some fixed sets of parameter values. This intricate phase space may bring some light to the understanding of these memristor properties. The analytical and numerical results obtained extend the analysis presented in {[}Itoh \& Chua, 2009; Messias et al., 2010]. (AU)

• Processo FAPESP: 09/11699-0 - Oscilações Não-Lineares em Circuitos Elétricos e Aplicações no Estudo dos Memristores
• Beneficiário: Marluce da Cruz Scarabello
• Modalidade de apoio: Bolsas no Brasil - Mestrado
• Processo FAPESP: 12/18413-7 - Análise global de sistemas diferenciais polinomiais definidos no espaço R3
• Beneficiário: Marcelo Messias
• Modalidade de apoio: Auxílio à Pesquisa - Regular