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.

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We consider the escape from invariant sets of one-dimensional piecewise linear maps which are additively disturbed by weak Gaussian white noise. The escape rates from point attractors and from strange invariant sets in the vicinity of the crisis at fully developed chaos are analytically determined and compared with results from numerical simulations. Both situations are combined resulting in a model with a point attractor which has a strange invariant set as basin boundary. Numerically a nonexponentia1 decay of the attractor is found that can be described by a Markovian three-state model with transition rates known from the previous analysis. PACS number(s): 05.40. +j, 05.45.+b, 02.50. r tions in Sec. V.