A Finite-Dimensional Dynamical Model for Gelation in Coagulation Processes

Summary. We study a finite-dimensional system of ordinary differential equations derived from Smoluchowski's coagulation equations and whose solutions mimic the behaviour of the nondensity-conserving (geling) solutions in those equations. The analytic and numerical studies of the finite-dimensional system reveals an interesting dynamic behaviour in several respects: Firstly, it suggests that some special geling solutions to Smoluchowski's equations discovered by Leyvraz can have an important dynamic role in gelation studies, and, secondly, the dynamics is interesting in its own right with an attractor possessing an unexpected structure of equilibria and connecting orbits. Received April 26, 1997; revised October 3, 1997; accepted October 23, 1997