Nonequilibrium phase transitions in stochastic systems with and without time delay: controlling various attractors with noise

Statistical behavior of ensembles of nonlinearly coupled elements driven by external noise is studied on the basis of nonlinear Fokker-Planck equations. The models incorporate two kinds of noise, the Langevin noise and the colored noise introduced in the coupling strength, and time delays. Various types of nonequilibrium phase transitions including Hopf bifurcations and transitions between limit cycle and chaos are shown to occur as the noise level is changed.