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We describe a new phenomenon in models of coalescence and fragmentation, thatof gel-shatter cycles. These are dynamical, unforced, stochastic cycles inwhich slow, approximately deterministic coalescence up to and beyond gelationis followed by abrupt random shattering. We describe their appearance insimulations of stochastic models with multiplicative kernels for coalescenceand spontaneous fragmentation into monomers (`shattering'). The regime in whichsuch cycles occur is characterized by a cyclicity order parameter, and weprovide a simple scaling argument which describes both this regime and thosewhich border it.

Stochastic gel-shatter cycles in coalescence-fragmentation models