Physical Review Letters · 1997 · 1.3K citations · 22 references
Natural SciencesMathematicsComplex SystemsDynamical SystemsSystem DynamicsBifurcation TheoryChaos TheoryDissipative SystemsNonlinear DynamicsOscillatorsChaotic DynamicsChaotic OscillatorsCoupled Oscillator DynamicsCoupled Oscillator SystemsCoupled OscillatorsLyapunov SpectrumSynchronizationSynchronization Transitions
We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe this regime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.
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Synchronization in chaotic systems
Louis M. Pecora, Thomas L. Carroll · Physical Review Letters · 1990 · 10.6K citations
An equation for continuous chaos
Otto E. Rössler · Physics Letters A · 1976 · 4K citations