Delay-induced Hopf bifurcation in the double-link inverted pendulum system for human quiet standing

A time delay double inverted pendulum model is built to represent a human in quiet standing postural control. A linear stability analysis for the trivial equilibrium is firstly considered. A delay-induced supercritical Hopf bifurcation happens at critical time delay point. The bifurcating periodic solution is calculated analytically by using the method of multiple scales. The reaction speed of brain, namely, the time delay is considered as bifurcation parameters to investigate the effect on the dynamical behaviors when human quiet standing. It shows that a person with slow reaction is easy to lose the stability of his/her quiet standing. The validity of the theoretical analysis is shown by their consistency with the numerical simulation.