Abstract

SUMMARY leaves the domain of attraction of equilibrium point i for the domain of attraction of equilibrium point j.When a dynamical system with multiple equilibrium Define the finite state Markov process z(T) on the state points is perturbed by continous wide-band noise, it is space {xl,..xn by its infinitesimal transition rate known that transitions between different equilibrium points occur with probability one. An important pro-blem associated with the analysis of these systems is ij ij) () (2)the statistical characterization of the jump process which represents the transitions between different do- hi(E) mains of attraction. A physical example of a dynamical system with multiple equilibrium point are common is an The main result can be stated as follows: interconnected power system, where the swing equations Let A(xt) = xi if xt is in the domain of attraction [1] represent a system with many possible equilibrium iof the equilibrium point x angles, defined by a power balance between electrical supply and demand. When the demand fluctuations and Define the initial distribution of z(o) as: unmodeled effects are represented as additive random noise, the resulting system undergoes transitions be- rz(o)- p A() =