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On-Off Intermittency: General Description and Feedback Model

Published online by Cambridge University Press:  11 May 2010

M. R. E. Proctor
Affiliation:
University of Cambridge
P. C. Matthews
Affiliation:
University of Cambridge
A. M. Rucklidge
Affiliation:
University of Cambridge
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Summary

There is a large number of physical phenomena exhibiting a peculiar behavior: the system is quiescent for long periods followed by a burst of activity. This behavior is persistent, and can be characterized by intermittent switching of system variables. A general model describing intermittent behavior has been found. The simplest version of On-Off intermittency does not involve feedback of the intermittent signal into the forcing function which makes it unrealistic in most physical situations. This paper discusses a method of putting feedback into the system and its applications to simple dynamical systems.

INTRODUCTION

Chaotic dynamical systems can be grouped into two classes according to the characteristics of their behavior. One class is characterized by aperiodic modulations of already periodic signals while the other class is characterized by signals which exhibit apparently random switching between qualitatively different kinds of behavior. The latter behavior is called intermittency. Examples of intermittency are abundant in nature. They include intermittent bursts of turbulence in otherwise laminar pipe flow in fluid dynamics, sunspot activity in astrophysics, and stock market crashes in economics. A model of intermittency in terms of dynamical systems as well as a partial classification of some types of intermittency was given by Pomeau & Manneville (1980). In general, signals produced by this scenario are periodic oscillations interrupted from time to time by some aperiodic bursts of activity. Another model of intermittency, crisis-induced intermittency, was introduced by Grebogi, Ott, Romeiras & Yorke (1987). This intermittency involves a collision in phase- space of two chaotic attractors as some parameter is varied, and it is again characterized by random switching between different aperiodic oscillations.

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Publisher: Cambridge University Press
Print publication year: 1994

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