Active control with delay of catastrophic motion and horseshoes chaos in a single well Duffing oscillator

In this paper, the control of escape and Melnikov chaos of an harmonically excited particle from a catastrophic (unbounded) single well φ4 potential is considered. In the linear limit, the range of the control gain parameter leading to good control is obtained and the effect of time delays on the control force is taken into account. The approximate critical external forcing amplitudes for catastrophe and chaos are obtained by using the energy and Melnikov methods. The control efficiency is found by analysing the behaviour of the external critical forcing amplitude of the controlled system as compared to that of the uncontrolled system.