Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays

Discrete Breathers, which are dynamical localizations of energy observed in the response of periodic, discrete Hamiltonian lattices to external forcing, have been recently observed in the response of micro-scale cantilever arrays. In this article, the authors invoke an analytical formalism introduced in their previous work to study the influence of white noise excitation on the formation and destruction of discrete breathers in a micro-scale cantilever array with strong intersite nonlinearities. The Fokker-Planck equation for a typical element of the array is derived. Numerical solutions to a system of approximate moment evolution equations obtained from the Fokker-Planck equation elucidate the influence of noise of varying intensity on the emergence and sustenance of discrete breathers in the array. The reported results can form the basis for developing a fundamental understanding of the influence of noise on breathers in coupled arrays of nonlinear oscillators with strong intersite nonlinearities including arrays of microelectromechanical systems.