Stochastic gel-shatter cycles in coalescence-fragmentation models

¹ Department of Mathematics, University of York - York, YO10 5DD UK
² Department of Biology, University of York - York, YO10 5DD UK

Received: 30 September 2020
Accepted: 19 February 2021

Abstract

We describe a new phenomenon in models of coalescence and fragmentation, that of gel-shatter cycles. These are dynamical, unforced, stochastic cycles in which slow, approximately deterministic coalescence up to and beyond gelation is followed by abrupt random shattering. We describe their appearance in simulations of stochastic models with multiplicative kernels for coalescence and spontaneous fragmentation into monomers (“shattering”). The regime in which such cycles occur is characterized by a cyclicity order parameter, and we provide a simple scaling argument which describes both this regime and those which border it.