Regimes in Simple Systems

Abstract Dynamical systems possessing regimes are identified with those where the state space possesses two or more regions such that transitions of the state from either region to the other are rare. Systems with regimes are compared to those where transitions are impossible. A simple one-dimensional system where a variable is defined at N equally spaced points about a latitude circle, once thought not to possess regimes, is found to exhibit them when the external forcing F slightly exceeds its critical value F* for the appearance of chaos. Regimes are detected by examining extended time series of quantities such as total energy. A chain of k* fairly regular waves develops if F < F*, and F* is found to depend mainly upon the wavelength L* = N/k*, being greatest when L* is closest to a preferred length L0. A display of time series demonstrates how the existence and general properties of the regimes depend upon L*. The barotropic vorticity equation, when applied to an elongated rectangular region, exhibits...