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We study the effects of noise cross-correlations on the steady states ofdriven, nonequilibrium systems, which are described by two stochasticallydriven dynamical variables, in one dimension. We use a well-knownstochastically driven coupled model with two dynamical variables, where one ofthe variables is autonomous being independent of the other, whereas the secondone depends explicitly on the former. Introducing cross-correlations of the twonoises in the two dynamical equations, we show that depending upon the detailsof the nonlinear coupling between the dynamical fields, such cross-correlationscan induce instabilities in the models, that are otherwise stable in theabsence of any cross-correlations. { We argue that this is reminiscent of theroughening transition found in the Kardar-Parisi-Zhang equation in dimensionsgreater than two.} Phenomenological implications of our results are discussed.

Noise crosscorrelations can induce instabilities in coupled driven models