Memory Effects and Scaling Laws in Slowly Driven Systems

Nils Berglund and Hervé Kunz
J. Phys. A 32 15-39 (1999)

This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently occur in these systems. The examples include the delayed appearance of convection rolls in Rayleigh-Bénard convection with slowly varying temperature gradient, scaling of hysteresis area for ferromagnets in a low-frequency magnetic field, and a pendulum on a rotating table displaying chaotic hysteresis. A mathematical theory is outlined, which allows to prove existence of hysteresis cycles, and determine related scaling laws.

Keywords and phrases: adiabatic theory, slow-fast systems, bifurcation theory, dynamic bifurcations, bifurcation delay, hysteresis, metastability, scaling laws.


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