Challenger Joseph D, Fanelli Duccio, McKane Alan J
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze and INFN, via Sansone 1, IT 50019 Sesto Fiorentino, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Oct;88(4):040102. doi: 10.1103/PhysRevE.88.040102. Epub 2013 Oct 22.
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 nonchaotic 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.
我们开发了一种通用形式主义，以构建一个马尔可夫链模型，该模型在无限种群极限下收敛到一个一维映射。因此，随机波动是系统内部的，而非外部指定的。对于有限种群，设计了一种近似高斯方案来描述非混沌区域中的随机波动。更一般地，可以使用通过对马尔可夫链进行近似得到的随机差分方程来捕捉随机动力学。以逻辑斯谛映射为例对该方案进行了演示。
