THE VARIABLE STRUCTURE SYSTEM: INTERMITTENCY, CHAOS, AND TRAPPING IN ELECTRONIC EXPERIMENTS AND SIMULATIONS

D.J. Jefferies and J.H.B. Deane
School of Electronic Engineering,
Information Technology, and Mathematics
University of Surrey
Guildford GU2 5XH
UK
d.jefferies@ee.surrey.ac.uk
http://www.ee.surrey.ac.uk/Personal/D.Jefferies/

Abstract:

The concept of a Variable Structure System (VSS), in which the structure is determined by the dynamical response, is described and measurements and simulations on VSSs comprising electronic systems which display bursty chaotic or ``intermittent" behaviour, and also on a network traffic transfer protocol, which is demonstrated to be a VSS in the same sense, are used to support the thesis that such bursty behaviour is common in such systems. An example of trapping in a two-centre system is given to show that the ideas can be extended to continuous-variable dynamical systems having piecewise-linear properties. The studies of these simple electronic systems provide insight for cases where similar behaviour of a time series is observed in other complex systems; some other VSSs are listed and their properties are considered.

• Introduction
  • Background
  • Purpose of the paper
  • Definitions
• VSS examples - 1: Electronic iterating circuits used to demonstrate ``crisis-induced" intermittency
  • The iteration system
  • Features
  • Crisis-induced intermittency
  • Simulation
  • Circuits
  • Experiments
• VSS examples - 2: Two-centre and impacting systems
• VSS examples - 3: Network dynamics - computer simulations
• Discussion
• Conclusions
• References
• About this document ...