Novel bifurcation structure generated in piecewise-linear three- resonant circuit and its Lyapunov analysis

Munehisa Sekikawa, Naohiko Inaba, Takashi Tsubouchi, Kazuyuki Aihara

doi:10.1016/j.physd.2012.03.011

Novel bifurcation structure generated in piecewise-linear three- resonant circuit and its Lyapunov analysis

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書誌事項

公開日: 2012-07

権利情報

https://www.elsevier.com/tdm/userlicense/1.0/

DOI

10.1016/j.physd.2012.03.011

公開者: Elsevier BV

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説明

Abstract We analyse a piecewise-linear oscillator that consists of a three- L C resonant circuit with a hysteresis element. Three sets of two-dimensional linear equations, including a hysteresis function, represent the governing equations of the circuit, and all the Lyapunov exponents are calculated in a remarkably simple manner based on derived explicit solutions. Various dynamical phenomena such as two-torus, three-torus, and hyperchaos with four positive Lyapunov exponents are observed by Lyapunov analysis. We obtained a detailed bifurcation diagram in which novel bifurcation structure which we call a “two-torus Arnold tongue” is observed where two-torus generating regions exist in a three-torus generating region as if periodic states exist in a two-torus generating region.