Deterministic Noise Amplifiers

Abstract:

Although we are accustomed to considering only overall stability properties of dynamical systems, local stability properties can also have a dramatic physical effect. Local instabilities in overall stable motion can cause otherwise imperceptible ambient noise to be amplified to macroscopic proportions. The result can be easily mistaken for deterministic chaos. We give measures for local instability and noise amplification in terms of the covariance matrix and local divergence rates and analyze several examples. An experimental test can be made by varying the external noise level; for sufficiently small amplitudes, the noisy response due to local instabilities scales linearly with the noise level, whereas noisy behavior due to deterministic chaos is largely unaffected.