Pattern dynamics associated with on-off convection in a one-dimensional system.

A numerical and theoretical analysis of the phenomenologically constructed nonlinear stochastic model of on-off intermittency experimentally observed by John et al. in the electrohydrodynamic convection in nematic liquid crystal under applied dichotomous electric field is carried out. The model has the structure of the one-dimensional Swift-Hohenberg equation with a fluctuating threshold which represents an applied electric field and either with or without additive noise which corresponds to thermal noise. It is found that the fundamental statistics of pattern dynamics without additive noise agree with those experimentally observed, and also with those reported previously in two-dimensional system. In contrast to that the presence of multiplicative noise generates an intermittent evolution of pattern intensity, whose statistics are in agreement with those of on-off intermittency so far known, the additive noise gives rise to the change of position of the convective pattern. It is found that the temporal evolution of the phase suitably introduced to describe the global convective pattern also shows an intermittent evolution. Its statistics are studied in a detailed way with numerical simulation and stochastic analysis. The comparison of these results turn out to be in good agreement with each other.