Equivalence Between Motions with Noise-Induced Jumps and Chaos with Smale Horseshoes

by Michael Frey, Natl Inst of Standards and Techn, Gaithersburg, United States,
Emil Simiu, Natl Inst of Standards and Techn, Gaithersburg, United States,



Document Type: Proceeding Paper

Part of: Engineering Mechanics

Abstract: For certain sets of parameters multi-stable oscillators excited by noise can exhibit irregular jumps. We consider one-degree-of-freedom near-integrable multi-stable systems whose unperturbed flows have homoclinic/heteroclinic orbits. For such systems we show that certain motions with noise-induced jumps are in fact chaotic motions with traveling Smale horseshoe sequences. Consequences of our result are that noise can, by itself, induce such chaotic motions. In the presence of periodic or quasiperiodic excitation, noise cannot suppress chaotic motion that might otherwise occur; rather, its effect is to broaden the windows of chaotic behavior.

Subject Headings: Oscillations | Parameters (statistics) | Degrees of freedom | Orbits | Excitation (physics) | Windows | Vector analysis

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