Temporal oscillations in Becker-Doering equations with atomization

Abstract

We prove that time-periodic solutions arise via Hopf bifurcation in a finite closed system of coagulation-fragmentation equations. The system we treat is a variant of the Becker-Doering equations, in which clusters grow or shrink by addition or deletion of monomers. To this is added a linear atomization reaction for clusters of maximum size. The structure of the system is motivated by models of gas evolution oscillators in physical chemistry, which exhibit temporal oscillations under certain input/output conditions.

30 pages, 3 figures; revised to include formal continuum limit & minor revisions

References in corpus (4)

• Power-law versus exponential distributions of animal group sizes
• Oscillations in aggregation-shattering processes
• Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance
• Steady oscillations in aggregation-fragmentation processes

Cited by in corpus (7)

• Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics
• Hopf bifurcation in addition-shattering kinetics
• Origin of the spontaneous oscillations in a simplified coagulation-fragmentation system driven by a source
• Stability condition of the steady oscillations in aggregation models with shattering process and self-fragmentation
• Gelation in input-driven aggregation
• Model reduction in Smoluchowski-type equations
• Stochastic gel-shatter cycles in coalescence-fragmentation models