Nonresonant Hopf bifurcations of a controlled van der Pol–Duffing oscillator

[1]  Colin H. Hansen,et al.  Stability and dynamics of a controlled van der Pol-Duffing oscillator , 2006 .

[2]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[3]  Jun Jiang,et al.  The global bifurcation characteristics of the forced van der Pol oscillator , 1996 .

[4]  Z. Wang,et al.  Robust stabilization to non-linear delayed systems via delayed state feedback: the averaging method , 2005 .

[5]  Alejandro J. Rodríguez-Luis,et al.  Oscillation-sliding in a modified van der pol-duffing electronic oscillator , 2002 .

[6]  Wanda Szemplińska-Stupnicka,et al.  THE COEXISTENCE OF PERIODIC, ALMOST-PERIODIC AND CHAOTIC ATTRACTORS IN THE VAN DER POL-DUFFING OSCILLATOR , 1997 .

[7]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[8]  A. Maccari,et al.  Vibration control for parametrically excited Liénard systems , 2006 .

[9]  L. A. Belyakov,et al.  On Bifurcations of Periodic Orbits in the van der Pol-Duffing Equation , 1997 .

[10]  Andrew Y. T. Leung,et al.  Resonances of a Non-Linear s.d.o.f. System with Two Time-Delays in Linear Feedback Control , 2002 .

[11]  Jinchen Ji,et al.  Stability and bifurcation in an electromechanical system with time delays , 2003 .

[12]  Attilio Maccari.  Vibration control for the primary resonance of the van der Pol oscillator by a time delay state feedback , 2003 .

[13]  K. Liew,et al.  On the stability properties of a Van der Pol–Duffing oscillator that is driven by a real noise , 2005 .

[14]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[15]  Fatihcan M. Atay,et al.  VAN DER POL'S OSCILLATOR UNDER DELAYED FEEDBACK , 1998 .

[16]  Andrew Y. T. Leung,et al.  Bifurcation Control of a Parametrically Excited Duffing System , 2002 .

[17]  A. Maccari,et al.  The Response of a Parametrically Excited van der Pol Oscillator to a Time Delay State Feedback , 2001 .

[18]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[19]  Pei Yu,et al.  A perturbation method for computing the simplest normal forms of dynamical systems , 2003 .

[20]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .

[21]  Jinchen Ji,et al.  Local Bifurcation Control of a Forced Single-Degree-of-Freedom Nonlinear System: Saddle-Node Bifurcation , 2001 .

[22]  Jinchen Ji,et al.  Stability and Hopf bifurcation of a magnetic bearing system with time delays , 2003 .

[23]  Guanrong Chen,et al.  Bifurcation Control: Theories, Methods, and Applications , 2000, Int. J. Bifurc. Chaos.

[24]  Junjie Wei,et al.  Stability and bifurcation analysis in Van der Pol's oscillator with delayed feedback , 2005 .

[25]  Guanrong Chen,et al.  Resonance Control for a Forced Single-Degree-of-Freedom Nonlinear System , 2004, Int. J. Bifurc. Chaos.

[26]  John G. Milton,et al.  Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback , 1995 .