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Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor

Author

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  • Denis de Carvalho Braga
  • Luis Fernando Mello
  • Marcelo Messias

Abstract

We study the local codimension one, two, and three bifurcations which occur in a recently proposed Van der Pol-Duffing circuit (ADVP) with parallel resistor, which is an extension of the classical Chua's circuit with cubic nonlinearity. The ADVP system presents a very rich dynamical behavior, ranging from stable equilibrium points to periodic and even chaotic oscillations. Aiming to contribute to the understand of the complex dynamics of this new system we present an analytical study of its local bifurcations and give the corresponding bifurcation diagrams. A complete description of the regions in the parameter space for which multiple small periodic solutions arise through the Hopf bifurcations at the equilibria is given. Then, by studying the continuation of such periodic orbits, we numerically find a sequence of period doubling and symmetric homoclinic bifurcations which leads to the creation of strange attractors, for a given set of the parameter values.

Suggested Citation

  • Denis de Carvalho Braga & Luis Fernando Mello & Marcelo Messias, 2009. "Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-26, November.
    • Handle: RePEc:hin:jnlmpe:149563
    DOI: 10.1155/2009/149563
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    Cited by:

    1. A. E. Matouk & T. N. Abdelhameed & D. K. Almutairi & M. A. Abdelkawy & M. A. E. Herzallah, 2023. "Existence of Self-Excited and Hidden Attractors in the Modified Autonomous Van Der Pol-Duffing Systems," Mathematics, MDPI, vol. 11(3), pages 1-13, January.

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