Wednesday, June 5, 2013

1306.0837 (Joseph D. Challenger et al.)

Intrinsic noise and discrete-time processes    [PDF]

Joseph D. Challenger, Duccio Fanelli, Alan J. McKane
A general formalism is developed to construct a Markov chain model from a one-dimensional map. Stochastic fluctuations are therefore internal to the system and not externally imposed. The Markov chain converges to the deterministic map in the infinite population limit. For finite populations an approximate scheme is devised to describe the first two moments of the probability distribution. The accuracy of the analytical scheme is demonstrated numerically, using the logistic map. The intrinsic noise anticipates the edge of chaos and non-chaotic windows become chaotic in the stochastic regime.
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