Abstract
Multiple time scale arguments are used to show that near a Hopf bifurcation to a chemical oscillation the dynamics of the system reduces to that of a classic soluble limit cycle system. A birth and death master equation is then introduced and the spectrum of the resulting transition operator is shown to be complex. Exact solutions of the master equation are obtained both for the steady and (for a rather general class of systems) “excited” states. Thus a simple basis of universality of critical properties in chemical oscillations is provided.
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Research supported in part by a grant from the National Science Foundation.
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DelleDonne, M., Ortoleva, P. Critical fluctuation universality in chemically oscillatory systems: A soluble master equation. J Stat Phys 20, 473–486 (1979). https://doi.org/10.1007/BF01012895
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DOI: https://doi.org/10.1007/BF01012895