Abstract
Random perturbations of one dimensional bifurcation diagrams can exhibit qualitative behavior that is quite different from that of the unperturbed, deterministic situation. For Markov solutions of one dimensional random differential equations with bounded ergodic diffusion processes as perturbations, effects like disappearance of stationary Murkov solutions (‘break through’), slowing down, bistability, and random symmetry breaking can occur. These effects are partially the results of local considerations, but as the perturbation range increases, global dynamics can alter the picture as well. The results are obtained via the analysis of stationary solutions of degenerate Markov diffusion processes, of stationary, non-Markovian solutions of stochastic flows, and of Lyapunov exponents of stochastic flows with respect to steady states.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
