Nonlinear Fluctuations Associated with Instabilities in Dissipative Systems

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Abstract
Computer experiments are performed on a model system of coupled mode equations designed to represent the Gunn instability, in order to investigate the origin of anomalously large fluctuations observed often over a wide range beyond an instability point in a dissipative system. The experiments deal with a system of 40 modes which possesses a number of steady states (attractors) beyond the instability point. It is shown that the system travels in phase space along an erratic or chaotic trajectory for long time in the approach to one of these attractors from an unstable equilibrium point. According to the modern ergodic theory, trajectories are proved to be stochastic by demonstrating that they satisfy the exponential law of growth of stochastic instability, that is, they are unstable with respect to small disturbances. The system provides an example of rigidly deterministic systems whose dynamics are best described in stochastic terms. It is found that under the influence of random forces the system escapes from the reached attractor after fluctuating around it for some time and travels again along a long-lived stochastic trajectory. The system wanders erratically from attractor to attractor via macroscopically stochastic trajectories, which do not arise from external random forces, but from the nonlinearity inherent in the system. This wandering motion is observed as large fluctuations.

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