ROTATION SETS AND PHASE-LOCKING IN AN ELECTRONIC 3 OSCILLATOR SYSTEM

The parameter space of an electronic three oscillator system is invest igated and various codimension one and two bifurcations predicted by B aesens, Guckenheimer, Kim and MacKay are identified. Sampled time-seri es 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 syste m) using knowledge of where the invariant torus lies and the torus unf olding scheme of Ashwin and Swift. Examples of toroidal and annular ch aos are investigated by finding bounds on the size and shape of the ro tation set.