K. PatanarapeelertT. D. FrankR. FriedrichI. M. TangMahidol UniversityWestfalische Wilhelms-Universitat Munster2018-06-212018-06-212005-12-25Journal of Physics A: Mathematical and General. Vol.38, No.47 (2005), 10069-10083030544702-s2.0-27844606876https://repository.li.mahidol.ac.th/handle/123456789/16640We show the conditions under which nonlinear time-delayed dynamical systems with multiplicative noise sources can be transformed into linear time-delayed systems with additive noise sources. We show that, for such reducible systems, analytical expressions for stationary distributions can be obtained. We demonstrate that fluctuation-dissipation relations of reducible systems become trivial and we show that reducible systems may exhibit delay- and noise-induced transitions to bistability and secondary transitions to non-stationarity. Our general findings are exemplified for three models: a Gompertz model, a Hongler model and a model involving a 1 - x2 noise amplitude. © 2005 IOP Publishing Ltd.Mahidol UniversityMathematicsPhysics and AstronomyArticleSCOPUS10.1088/0305-4470/38/47/002