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

Abstract

A Fokker–Planck description for globally coupled many-body systems with time delayswas developed by integrating previously derived Fokker–Planck equations formany-body systems and for time-delayed systems. By means of the Fokker–Planckdescription developed, we examined the dependence of the variability of many-bodysystems on attractive coupling forces and time delays. For a fundamental classof systems exemplified by a time-delayed Shimizu–Yamada model for muscularcontractions, we established that the variability is an invertible one-to-one mapping ofcoupling forces and time delays and that coupling forces and time delays haveopposite effects on system variability, allowing time delays to annihilate the impactof coupling forces. Furthermore, we showed how variability measures could beused to determine coupling parameters and time delays from experimental data.