Coupled systems with quasi-periodic and chaotic dynamics

The interaction of a system with quasi-periodic autonomous dynamics and a chaotic Ro center dot ssler system is studied. We have shown that with the growth of the coupling, regimes of two-frequency and three-frequency quasipe-riodicity, a periodic regime and a regime of oscillation death sequentially arise. With a small coupling strength, doubling bifurcations of three-frequency tori are observed in the system. A chaotic regime, characterized by two additional zero Lyapunov exponents in spectrum, is revealed. Two-parameter Lyapunov exponent analysis and bifurcation analysis are presented. A new bifurcation scenario of transition from the regime of oscillation death to quasi-periodicity in coupled systems is described.

Automated summary

The interaction between a system with quasi-periodic autonomous dynamics and a chaotic Rössler system is studied. The coupling growth leads to the emergence of two-frequency and three-frequency quasi-periodicity, periodicity, and oscillation death in sequence. The system exhibits doubling bifurcations of three-frequency tori with small coupling strength. A chaotic regime with two additional zero Lyapunov exponents in the spectrum is discovered. Two-parameter Lyapunov exponent analysis and bifurcation analysis are conducted, and a new bifurcation scenario from oscillation death to quasi-periodicity in coupled systems is described.