Minimum-action paths for wave-number selection in nonequilibrium systems

The problem of wave-number selections in nonequilibrium pattern-forming systems in the presence of noise is investigated. The minimum-action method is proposed to study the noise-induced transitions between the different spatiotemporal states by generalizing the traditional theory previously applied in low-dimensional dynamical systems. The scheme is shown as an example in the stabilized Kuramoto-Sivashinsky equation. The present method allows us to conveniently find the unique noise selected state, in contrast to previous work using direct simulations of the stochastic partial differential equation, where the constraints of the simulation only allow a narrow band to be determined