A finite-dimensional dynamical model for gelation in coagulation processes

Summary. We study a finite-dimensional system of ordinary differential equations de-rived from Smoluchowski’s coagulation equations and whose solutions mimic the be-haviour of the nondensity-conserving (geling) solutions in those equations. The analytic and numerical studies of the finite-dimensional system reveals an inter-esting dynamic behaviour in several respects: Firstly, it suggests that some special geling solutions to Smoluchowski’s equations discovered by Leyvraz can have an important dy-namic 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. 1