Chaotic and Bifurcating Nonlinear Systems Driven by Noise with Applications to Laser Dynamics.

摘要

One aspect of the research work was focused on the effects of noise as a driving force in various nonlinear dynamical systems. Effects studied were postponements of bifurcations, state dependent diffusion, a mean first passage time in a system with both random temporal forcing in a random potential, a mean first passage time problem with colored noise. A second aspect involved studies on switching properties of nonlinear systems in the presence of noise, and a special application of the results to a noise quenched, correlated, spontaneous emission laser. A third major effort was devoted to studies on stochastic resonance (SR), with a remark on the theory, a long work on the use of analog simulations in studies of SR, a study on order and disorder in SR. At this point, a study was done on noise induced topological transitions in the two-dimensional stationary probability density of an archetypal bistable system. Finally, a new quantity was introduced to general studies on SR: the escape time probability distribution, wherein the theory, digital and analog simulations were accomplished. These new studies hold great promise for applications in a number of fields, including the creation of a deeper understanding of how noise assisted information is transmitted in biological neurons.