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Multiple-period-doubling bifurcation route to chaos in periodically pulsed chaotic oscillators. (English) Zbl 1225.70017
Ladde, G.S.(ed.) et al., Dynamic systems and applications. Volume 4. Proceedings of the 4th international conference, Morehouse College, Atlanta, GA, USA, May 21–24, 2003. Atlanta, GA: Dynamic Publishers (ISBN 1-890888-00-1/hbk). 80-86 (2004).
Summary: We consider the effect of periodically pulsed forcing on chaotic dynamical systems and show that the systems undergo novel multiple-period-doubling bifurcations prior to the onset of chaos. In the chaotic regime, the systems exhibit a rich variety of dynamical behaviour including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures and so on. For certain types of periodic pulses, the systems also admit transcritical bifurcations preceding the onset of multiple-period doubling behaviour. Here, we consider the Duffing oscillator and Duffing-van der Pol (DVP) oscillator as model systems and demonstrate that they exhibit the above mentioned novel properties.
For the entire collection see [Zbl 1054.34001].
MSC:
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
70K50 Bifurcations and instability for nonlinear problems in mechanics
70K40 Forced motions for nonlinear problems in mechanics
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