Stochastic Resonance in the Fermi-Pasta-Ulam Chain

Abstract

We consider a damped $\beta$-Fermi-Pasta-Ulam chain, driven at one boundary subjected to stochastic noise. It is shown that, for a fixed driving amplitude and frequency, increasing the noise intensity, the system's energy resonantly responds to the modulating frequency of the forcing signal. Multiple peaks appear in the signal to noise ratio, signalling the phenomenon of stochastic resonance. The presence of multiple peaks is explained by the existence of many stable and metastable states that are found when solving this boundary value problem for a semi-continuum approximation of the model. Stochastic resonance is shown to be generated by transitions between these states.

References in corpus (7)

• Discrete Breathers
• Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model
• On modulational instability and energy localization in anharmonic lattices at finite energy density
• The Anti-FPU Problem
• Bistability in sine-Gordon: the ideal switch
• Interaction of a Kink-Soliton with a Breather in a Fermi-Pasta-Ulam Chain
• Bistable light detectors with nonlinear waveguide arrays

Cited by in corpus (6)

• Emergent Bistability and Switching in a Nonequilibrium Crystal
• Nucleation of breathers via stochastic resonance in nonlinear lattices
• Thermostatistics in the neighborhood of the $\pi$-mode solution for the Fermi-Pasta-Ulam $\beta$ system: from weak to strong chaos
• Propagation dynamics on the Fermi-Pasta-Ulam lattices
• Stochastic resonance in a model of a periodically driven DNA : Multiple transitions, scaling and sequence dependence
• NySALT: Nyström-type inference-based schemes adaptive to large time-stepping