An analytical study for controlling unstable periodic motion in magneto-elastic chaos

A magneto-elastic beam system is described by the Duffing equation with delay feedback term. The perturbation technique leads to a general unstable periodic solution near the homoclinic orbit of the equation. A necessary and sufficient condition for stabilizing the solution is given as the relation between control parameters and initial constants, It is shown that sensitivity of the solution to initial constants implies chaos and fitting the parameters to the condition can control the chaos. Good agreement is found between the analytical results and previous experimental facts. (C) 1997 Elsevier Science B.V.