@article {IOPORT.06080969,
    author       = {Sekikawa, Munehisa and Inaba, Naohiko and Tsubouchi, Takashi and Aihara, Kazuyuki},
    title        = {Novel bifurcation structure generated in piecewise-linear three-$LC$ resonant circuit and its Lyapunov analysis.},
    year         = {2012},
    journal      = {Physica D},
    volume       = {241},
    number       = {14},
    issn         = {0167-2789},
    pages        = {1169-1178},
    publisher    = {Elsevier Science B.V. (North-Holland), Amsterdam},
    doi          = {10.1016/j.physd.2012.03.011},
    abstract     = {Summary: We analyse a piecewise-linear oscillator that consists of a three-LC 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.},
    identifier   = {06080969},
}