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

*(English)*Zbl 1071.37061Summary: The control of escape and Melnikov chaos of an harmonically excited particle from a catastrophic (unbounded) single well \(\phi^4\) 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.

##### MSC:

37N35 | Dynamical systems in control |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

93C10 | Nonlinear systems in control theory |

70Q05 | Control of mechanical systems |

70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |

37N05 | Dynamical systems in classical and celestial mechanics |

##### Keywords:

control of escape; Melnikov chaos; potential; time delays; critical forcing amplitudes; catastrophe
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\textit{B. R. Nana Nbendjo} et al., Chaos Solitons Fractals 23, No. 3, 809--816 (2005; Zbl 1071.37061)

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##### References:

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