Controlling chaos of the forced pendulum with the OGY method

A number of methods to control the phenomenon of chaos in nonlinear dynamical systems have been reported. Of these, the technique known as the OGY method, devised by Ott, Grebogi and Yorke (1990) has attracted attention as one which can confine the desired periodic motion with the application of a small external force. In our research, we have applied the OGY method to a forced pendulum with a cyclic external force applied in the horizontal direction, as a nonlinear dynamical system with a more complex structure than that of the Lorentz attractor. We first investigate in detail using bifurcation diagrams and Lyapunov exponents, the regions in which chaos occurs in a forced pendulum. We then present some issues related to the target focal point of the periodic orbit, which is needed in particular to execute control using the OGY method