Rotation sets and phase-locking in an electronic three oscillator system. (English) Zbl 0784.34027
Summary: The parameter space of an electronic three oscillator system is investigated and various codimension one and two bifurcations predicted by Baesens, Guckenheimer, Kim and MacKay are identified. Sampled time- series from the experimental systems are recorded and analysed for partial mode-locking or resonance (one or two independent rational relations between the average rates of change of the angles describing the system) using knowledge of where the invariant torus lies and the torus unfolding scheme of Ashwin and Swift. Examples of toroidal and annular chaos are investigated by finding bounds on the size and shape of the rotation set.
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Keywords:
electronic three oscillator system; codimension one and two bifurcations; invariant torus; toroidal and annular chaos; rotation setReferences:
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