This study shows that the states with the minimum dissipation rate in general dissipative dynamic systems are expressed by the eigenfunctions for the dissipative dynamic operators. These eigenfunctions are shown to constitute the self-organized and self-similar decay phase as the attractor of the dissipative structure. A typical example applied to incompressible viscous fluid is presented to describe a physical picture of self-organization and bifurcation of the dissipative structure.

• Received 17 December 1992

DOI:https://doi.org/10.1103/PhysRevE.48.2975