We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling, we find for infinitely many constituents the coexistence of several ergodic components and a bifurcation behavior like in first-order phase transitions. These results are compared with simulations for finite systems both for global coupling and for nearest-neighbor coupling on two-and three-dimensional cubic lattices. The mean-field-type results for global coupling provide a better understanding of the more complex behavior in the latter case.

We describe nonequilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or antiferromagnetic ordered states. We discuss the phase diagram, the order of the transitions, and the critical behavior. For global coupling we show analytically that the critical exponent of the magnetization exhibits a transition from the value 1/2 to a nonuniversal behavior depending on the ratio of noise strength to the magnitude of the spatial coupling.

We propose a generalization of the Ornstein-Uhlenbeck process in 1+1 dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponentially decaying autocorrelation. The generalized Langevin equation of the process, the corresponding Fokker-Planck equation, and a discrete integral algorithm for numerical simulation are given. The process is an alternative to a recently proposed spatiotemporal correlated model process [J. García-Ojalvo et al., Phys. Rev. A 46, 4670 (1992)] for which we calculate explicitly the hitherto unknown autocorrelation function in real space.

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