Dynamical properties of Duffing-van der Pol oscillator subject to both external and parametric excitations with time delayed feedback control

In this paper, the nonlinear dynamical characteristics of the Duffing-van der Pol oscillator subject to both external and parametric excitations with time delayed feedback control are analyzed. Using the multiple scale method, the primary and principal parametric resonances are discussed. Both the periodic and chaos dynamical behaviors are presented by numerical solutions. From the results, it can be seen that the frequency and amplitude responses for the primary and principal parametric resonances can be affected by the time delayed control. Moreover, it is not only the external and parametric excitations that have an influence on the periodic and chaotic motions, but also the control parameters.