Ann. Phys. Fr.
Volume 19, Number 6, 1994
|Page(s)||691 - 714|
|Published online||01 June 2004|
Nonlinear Dynamics of Coupled Oscillators
Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, URA 1325 du CNRS, GDR 1023, 46 allée d'Italie, 69364 Lyon
Many nonlinear phenomena can be described and understood using the example of a one-dimensional array of coupled oscillators in the continuous limit. In the conservative case, we introduce the concept of amplitude equation and describe side-band instabilities. For parametrically forced dissipative systems, we discuss pattern formation and the secondary instabilities which trace back to broken symmetries at the primary instability onset. We consider the cases of broken translational invariance, which leads to the Eckhaus instability, and of broken parity which generates drifting patterns.
PACS: 0547 – Nonlinear dynamical systems and bifurcations / 0320 – Classical mechanics of discrete systems: general mathematical aspects
Key words: classical mechanics / nonlinear dynamical systems / oscillations / pendulums / solitons / coupled oscillators / nonlinear dynamics / one dimensional array / amplitude equation / side band instabilities / pattern formation / secondary instabilities / broken translational invariance / Eckhaus instability / broken parity / drifting patterns
© EDP Sciences, 1994