Strange attractors and chaos control in a Duffing–Van der Pol oscillator with two external periodic forces

Abstract An anharmonic Duffing–Van der Pol oscillator with two external forces is considered. By applying numerical results, strange attractors are presented and the chaotic behaviour is investigated. The problem of directing a chaotic state of the system to a periodic orbit is studied. By assuming that the exact model of the system is not known and that the position is the only state available for measurements, the controller comprises a linearizing-like feedback and an estimator. Simulations are provided to illustrate the performance of the controller.

[1]  Mikhail M. Sushchik,et al.  BISTABLE PHASE SYNCHRONIZATION AND CHAOS IN A SYSTEM OF COUPLED VAN DER POL DUFFING OSCILLATORS , 1999 .

[2]  W. Freeman.  The physiology of perception. , 1991, Scientific American.

[3]  K. Yagasaki.  Homoclinic motions and chaos in the quasiperiodically forced van der Pol-Duffing oscillator with single well potential , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[4]  Wanda Szemplińska-Stupnicka,et al.  Neimark bifurcation, almost-periodicity and chaos in the forced van der Pol-Duffing system in the neighbourhood of the principal resonance , 1994 .

[5]  C. Tchawoua,et al.  Exponential stabilization of two nonlinearly coupled oscillators by an estimated state feedback , 2002 .

[6]  Zheng-Ming Ge,et al.  Chaos, chaos control and synchronization of a gyrostat system , 2002 .

[7]  K. Yagasaki.  Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems , 1993 .

[8]  Balth. van der Pol,et al.  VII. Forced oscillations in a circuit with non-linear resistance. (Reception with reactive triode) , 1927 .

[9]  G. Sallet,et al.  Exponential Stabilization of Nonlinear Systems by an Estimated State Feedback , 1993 .

[10]  E. A. Jackson,et al.  Perspectives of nonlinear dynamics , 1990 .

[11]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[12]  Ricardo Femat,et al.  On robust chaos suppression in a class of nondriven oscillators: application to the Chua's circuit , 1999 .

[13]  P. Kokotovic,et al.  The peaking phenomenon and the global stabilization of nonlinear systems , 1991 .

[14]  Leon O. Chua,et al.  ADAPTIVE SYNCHRONIZATION OF CHUA'S OSCILLATORS , 1996 .

[15]  M. Lakshmanan,et al.  Chaos in Nonlinear Oscillators: Controlling and Synchronization , 1996 .

[16]  M. Lakshmanan,et al.  Bifurcation and chaos in the double-well Duffing–van der Pol oscillator: Numerical and analytical studies , 1997, chao-dyn/9709013.