Bifurcations and chaos of a particular van der Pol-Duffing oscillator. (English) Zbl 1235.70114
Summary: We present chaotic dynamics of a particular non-linear oscillator having Duffing type stiffness, van der Pol damping and dry friction. We first utilize an averaging technique to obtain informations regarding the bifurcation behaviour of the vibrating system and then we analyze numerically the chaotic behaviour of the oscillator for parameters near bifurcation curves. We also discuss and illustrate the influence of the dry friction on the behaviour of a strange chaotic attractor.
MSC:
70K50 | Bifurcations and instability for nonlinear problems in mechanics |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
37G99 | Local and nonlocal bifurcation theory for dynamical systems |