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Successive torus doubling and birth of strange non-chaotic attractors in non-linear electronic circuit

Successive torus doubling and birth of strange non-chaotic attractors in non-linear electronic circuit

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The authors experimentally demonstrate successive torus doubling and the birth of strange non-chaotic attractors (SNAs) in a quasi-periodically forced Chua's oscillator. So far it has been believed that the torus doubling occurs only a finite number of times. In this Letter, the authors report experimental observation of a certain kind of torus doubling called swollen shape bifurcation occurs an infinite number of times and leads to the birth of SNA. In the Poincaré of the section, the torus undergoes a series of period doubling and after a particular value of control parameter, the infinitely period doubled torus in the localised regime termed as a chaotic band. While the Lyapunov exponent of the attractor has a negative value and confirms the attractor becomes strange and non-chaotic. Experimentally observed results are confirmed by a Poincaré map, singular-continuous spectrum analysis and the finite-time Lyapunov exponent.

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      • 5. Feudel, U., Kuznetsov, S., Pikovsky, A.: ‘Strange nonchaotic attractors: dynamics between order and chaos in quasiperiodically forced systems’ (World Scientific, Singapore, 2006).
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