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Quasi-periodic structures and "shrimps" in chaos on the example of a two-mode van der Pol generator
Alexander P Kuznetsov1, Igor R Sataev1, Nataliya V Stankevich2
1Laboratory of Theoretical Nonlinear Dynamics, Kotel'nikov's Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation.
Abstract:
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within these regions. Among them, structures known for periodic regimes as "shrimps" stand out. Within quasi-periodic shrimps, there are numerous bifurcations of doubling invariant tori, leading to a transition to chaos. The Poincaré sections for different quasi-periodic windows correspond to invariant curves with distinct numbers of turns.
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