Memory effects and scaling laws in slowly driven systems

This paper 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-Benard 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 us to prove the existence of hysteresis cycles, and determine related scaling laws.