Intrinsic noise and discrete-time processes
Statistical Mechanics
2014-09-15 v2 Chaotic Dynamics
Abstract
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For finite populations an approximate Gaussian scheme is devised to describe the stochastic fluctuations in the non-chaotic regime. More generally, the stochastic dynamics can be captured using a stochastic difference equation, derived through an approximation to the Markov chain. The scheme is demonstrated using the logistic map as a case study.
Cite
@article{arxiv.1306.0837,
title = {Intrinsic noise and discrete-time processes},
author = {Joseph D. Challenger and Duccio Fanelli and Alan J. McKane},
journal= {arXiv preprint arXiv:1306.0837},
year = {2014}
}
Comments
Modified version accepted for publication in Phys. Rev. E Rapid Communications. New figures added