Coherent noise, scale invariance and intermittency in large systems

Abstract

We introduce a new class of models in which a large number of "agents" organize under the influence of an externally imposed coherent noise. The model shows reorganization events whose size distribution closely follows a power-law over many decades, even in the case where the agents do not interact with each other. In addition the system displays "aftershock" events in which large disturbances are followed by a string of others at times which are distributed according to a t −1 law. We also find that the lifetimes of the agents in the system possess a power-law distribution. We explain all of these results using an approximate analytic treatment of the dynamics and discuss a number of variations on the basic model relevant to the study of particular physical systems.

A Model for Evolution and Extinction

“…As the figure shows, the distribution of event sizes closely follows a power law, with an exponent of about −2 for all of these distributions. Sneppen and Newman 19 have explained this result using an approximate mean-field-like treatment of the model. It is possible to choose a distribution of the applied stresses that will not produce a power-law extinction size distribution (a uniform distribution between zero and one will not, for example), but the cases shown in Figure 4 cover most of the distributions likely to be found in nature.…”

Evolution and Extinction Dynamics in Rugged Fitness Landscapes

“…Available evolutionary data present a challenge for the theoretician, a challenge which has been recently taken up in several different approaches [1,2,11,12,13,14,15,16,17]. Starting from extremely simplified assumptions, these models make use of ideas and techniques borrowed form physics, particularly the statistical mechanics of interacting systems, in order to find quantitative predictions for evolutionary measures.…”

“…The distribution of life-times is a power-law with an exponent close to −1. A related paper by Sneppen and Newman [15] analyzes this model from a more technical point of view. The authors find that for a wide variety of noise distributions the event sizes are distributed as s −x , with x = 1 + α and α ≈ 1, slightly depending on the noise distribution.…”

Research of Newman’s Biological Evolution Model

“…Следуя работам [3][4][5][6][7][8], воспользуемся приближением среднего по-ля, пренебрегая флуктуациями распределения видов по устойчивости r( ). Темп его изменения с течением времени определяется формулой…”

“…Второй подход, базирующийся на том, что эволюция связана с экзогенными причинами, был развит М. Ньюманом в модели с ко-герентным шумом [3][4][5][6][7][8], исследованию которой посвящена настоя-щая работа. Модель построена в предположении отсутствия какого-либо взаимодействия между видами.…”