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Slow flow solutions and chaos control in an electromagnetic seismometer system

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  • Lazzouni, Sihem A.
  • Siewe Siewe, M.
  • Moukam Kakmeni, F.M.
  • Bowong, Samuel

Abstract

We study in this paper the dynamics and chaos control of a non-linear electromagnetic seismometer system consisting of an extended Duffing electrical oscillator magnetically coupled with a natural Duffing mechanical oscillator. The singular perturbation method is used to find slow solutions. Some bifurcation structures and the variation of the corresponding Lyapunov exponent are obtained. Transitions from a regular behavior to chaotic orbits are seen to occur for large amplitudes of the external excitation. We also examine the application of a simple adaptive damping feedback controller to eliminate the chaotic behavior in a controlled extended Duffing system. The main idea is to regulate the chaotic motion of the electromagnetic seismometer system around less complex attractors, such as equilibrium points and periodic orbits. The effectiveness and efficiency of the proposed feedback control strategy is illustrated by means of numerical simulations.

Suggested Citation

  • Lazzouni, Sihem A. & Siewe Siewe, M. & Moukam Kakmeni, F.M. & Bowong, Samuel, 2006. "Slow flow solutions and chaos control in an electromagnetic seismometer system," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 988-1001.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:4:p:988-1001
    DOI: 10.1016/j.chaos.2005.08.061
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    Cited by:

    1. Siewe, M. Siewe & Cao, Hongjun & Sanjuán, Miguel A.F., 2009. "Effect of nonlinear dissipation on the basin boundaries of a driven two-well Rayleigh–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1092-1099.

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