Fokker-Planck equations for globally coupled many body systems with time delays

A Fokker-Planck description for globally coupled many-body systems with time delays was developed by integrating previously derived Fokker-Planck equations for many-body systems and for time-delayed systems. By means of the Fokker-Planck description developed, we examined the dependence of the variability of many-body systems on attractive coupling forces and time delays. For a fundamental class of systems exemplified by a time-delayed Shimizu-Yamada model for muscular contractions, we established that the variability is an invertible one-to-one mapping of coupling forces and time delays and that coupling forces and time delays have opposite effects on system variability, allowing time delays to annihilate the impact of coupling forces. Furthermore, we showed how variability measures could be used to determine coupling parameters and time delays from experimental data. © 2005 IOP Publishing Ltd.