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Critical dynamics the expansion of the master equation including a critical point

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  • Dekker, H.

Abstract

The master equation for a general Markov process that shows a transition from monostable to bistable behaviour will be evaluated systematically in terms of a small parameter, namely the reciprocal size of the system. The expansion is uniformly valid also at the critical point. The fundamental idea is to separate the master equation into its irreducible part and a corrective remainder. The irreducible or zeroth order approximation is a relatively simple Fokker-Planck equation containing the essential features of the process. Having achieved complete knowledge of the eigensolutions of the irreducible equation the higher order corrections are computed explicitly.

Suggested Citation

  • Dekker, H., 1980. "Critical dynamics the expansion of the master equation including a critical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 80-98.
    • Handle: RePEc:eee:phsmap:v:103:y:1980:i:1:p:80-98
    DOI: 10.1016/0378-4371(80)90208-3
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