View source for Haken-Kelso-Bunz model

==Theoretical Predictions and Experimental Confirmation==

In HKB loss of stability, also called ''dynamic instability'', causes switching to occur. One is free to inquire about the location of 'switches' inside the system but that is not the key to understanding what is going on. Stability can be measured in several ways:
# Critical slowing down. If a small perturbation is applied to the system that drives it away from its stationary state, the time for the system to return to its stationary state (its local relaxation time) is a measure of its stability.  The smaller the local relaxation time, the more stable the attractor. The less stable the pattern the longer it should take to return to the established pattern. HKB--or more correctly its stochastic equivalent (Schöner, Haken & Kelso, 1986)--predicts critical slowing down. That is, if the antiphase pattern is actually losing stability as the control parameter of frequency is increased, the local relaxation time should increase as the system approaches the critical point. Excellent agreement with theory was obtained in careful experiments (Scholz & Kelso, 1989; Scholz, Kelso & Schöner, 1987).
# Critical fluctuations. A signature feature of non-equilibrium phase transitions in nature is the presence of critical fluctuations. If switching patterns of behavior is due to loss of stability, direct measures of fluctuations of the order parameter (relative phase) should be detectable as the critical point approaches. Experiments by Kelso et al. (1986) showed a striking enhancement of fluctuations (measured as the standard deviation of the continuous relative phase) for the antiphase pattern as the control parameter approached a critical value. No such increase was observed over the same parameter range for the in-phase pattern.