Neimark bifurcation, almost-periodicity and chaos in the forced van der Pol-Duffing system in the neighbourhood of the principal resonance. (English) Zbl 0961.34502
Summary: The occurrence of chaotic motion in the forced van der Pol-Duffing oscillator in a neighbourhood of the principal resonance is considered and interpreted in connection with subcritical Neimark bifurcation. Computer simulations and approximate analytical analysis confirm that the chaotic motion region forms a transition zone between two regular motions: the \(T\)-periodic and almost-periodic oscillations.
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C27 | Almost and pseudo-almost periodic solutions to ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37C55 | Periodic and quasi-periodic flows and diffeomorphisms |
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
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