Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1899652 | Physica D: Nonlinear Phenomena | 2012 | 10 Pages |
We analyse a piecewise-linear oscillator that consists of a three-LCLC 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.
► We investigate a three-LC resonant circuit with a hysteresis element. ► We calculate all Lyapunov exponents, and obtain a detailed bifurcation diagram. ► We discover novel bifurcation structure we call a “Two-torus Arnold tongue”—where two-torus generating regions exist in a three-torus generating region. ► Hyperchaotic attractor with four positive Lyapunov exponents are observed.