Experimental confirmation of the theory for critical exponents of crisis

Abstract We investigate the scaling of the average time τ between intermittent bursts for a chaotic system that undergoes a homoclinic tangency crisis, which causes a sudden expansion in the attractor. The system studied is a periodically driven (frequency f), nonlinear, magnetoelastic ribbon. The observed behavior of τ is well fit by a power-law scaling τ ∼| f − f c | − γ , where f = f c at the crisis. We identify the unstable periodic orbit mediating the crisis, and detemine its linearized eigenvalues from experimental data. The critical exponent γ found from the scaling of τ is shown to agree with that theoretically predicted for a two-dimensional map on the basis of the eigenvalues of the mediating periodic orbit.

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