Quasi-periodic structures and “shrimps” in chaos on the example of a two-mode van der Pol generator

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.