Abstract
Nicolis and Prigogine have shown that the Volterra-Lotka model taken as a Markovian stochastic process does not have a steady state, by considering the Fokker-Planck-type equation for small fluctuations. Here we use the exact master equation to show that the only steady state in the model is the trivial one.
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References
G. Nicolis and I. Prigogine,PNAS 68:2102 (1971).
G. Nicolis,J. Stat. Phys. 6:211 (1972).
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Most of this work was done while the author was at the Center for Particle Theory, University of Texas, Austin, Texas. At present he is partly supported by the Israeli Academy of Sciences.
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Reddy, V.T.N. On the existence of the steady state in the stochastic Volterra-Lotka model. J Stat Phys 13, 61–64 (1975). https://doi.org/10.1007/BF01012599
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DOI: https://doi.org/10.1007/BF01012599