Nonlinear Phenomena in Complex Systems, 2007, Vol.10, No.1, pp.92-97

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2007, Vol.10, No.1, pp.92-97

Flexibility of Regular and Chaotic Attractors.
Marko Marhl

A short review of recent results on the flexibility of regular and chaotic attractors is presented. In particular, we focus on those studies that analyse the flexibility of dynamical systems in response to external perturbations, such as singular pulses, periodic signals, and noise. First the mathematical measures for estimating the flexibility of regular and chaotic attractors are presented. Then the most important applications of measuring the flexibility of attractors are reviewed. In particular, we emphasise the importance of estimating the flexibility of attractors for determining coupling properties of oscillators, explaining the constructive and destructive role of noise in case of stochastic resonance, and estimating the possibility for an optimal chaos control. We discuss the most important applications of the general mathematical tools for analysing the behaviour of biological systems, in particular, cellular oscillators.
Key words: dynamical system, flexibility, coupling, stochastic resonance, chaos

Full text: Acrobat PDF (123KB)