✦ LIBER ✦

Time development of probability distributions for interacting species

✍ Scribed by Gerald Rosen

Publisher: Springer
Year: 1979
Tongue: English
Weight: 450 KB
Volume: 41
Category: Article
ISSN: 1522-9602
DOI: 10.1016/s0092-8240(79)90017-x

No coin nor oath required. For personal study only.

✦ Synopsis

A general solution to the dynamical equation for the probability distribution associated with n interacting species is obtained by employing the author's generic canonical expression for the rate functions. Interacting species models with limit-cycle dynamics and no stable equilibrium points feature probability distributions that are asymptotic for large values of t to Dirac B-distributions concentrated on the limit-cycles, as illustrated here for an analytically solvable two-species model. For an n-species Volterra model, a stationary or temporally-averaged probability distribution should generally be much more complicated than the specialized Poisson form studied by Kerner and others.

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