Dynamical transitions in a dissipative open system

The present model of a simple nonlinear dissipative system exhibits certain transition phenomena analogous to those studied experimentally by Chu and Goldstein (1973) in turbulent convection. Two types of transitions have so far been found in the model. The first is a bifurcation from a steady stable state to an unsteady quasi-periodic motion as the model Reynolds number passes through a critical value; the second transition occurs at a higher value of the model Reynolds number and involves a change from one class of unsteady motions to another class with symmetry properties. This dissipative system is found to exhibit a nontrivial statistical response to external forces.