TRANSITION TO CHAOS FROM A TWO-TORUS IN A DELAYED FEEDBACK SYSTEM

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Abstract
By using the center manifold and normal form theories of dynamical systems, we were able to show that when a "resonant" system, with a maximum in its amplitude Bode plot, is placed under delayed negative feedback, two-torus attractors appear near specific values of delay and feedback gain [Boe & Chang, 1989]. The two-torus attractors of a classical liquid-level control experiment with cascaded feedback are studied both numerically and experimentally here to complete the local analysis of the previous paper. Like other two-torus systems, we observe a Devil's staircase of frequency-locked tori with a fractal dimension 0.87. A torus-wrinkling mechanism for the transition to chaos, as proposed by Ostlund et al. [1983], is supported by our experiments.

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