DYNAMICS IN A CHAIN OF OVERDAMPED PENDULA DRIVEN BY CONSTANT TORQUES

This paper studies the dynamical behavior of a chain of overclamped pe ndula driven by constant torques with nearest neighbor coupling. The c oupling constant K is assumed to be >0, independent of M. It is shown that when the system does not have equilibrium points, the global attr actor of this system is a one-dimensional closed curve, so no matter w hat input frequencies w(j) are used, the existence, uniqueness, and gl obal stability of a limit cycle of second kind are proved; therefore, any solution will be frequency locked in the long time limit. On the o ther hand, if there are equilibrium points in the system, any solution is bounded and converges to an equilibrium point.