Persistence of three-frequency quasiperiodicity under large perturbations

The occurrence of quasiperiodic orbits in typical dissipative dynamical systems is of great importance. The equations for two driven coupled Van der Pol oscillators were integrated, and four Lyapunov exponents were calculated for every orbit. The results show that for small coupling and driving parameters, most orbits are three-frequency quasiperiodic. As the coupling and driving parameters are increased, three-frequency quasiperiodicity becomes less common, being first replaced by two-frequency quasiperiodicity, and then by periodic and chaotic motions. This example reinforces past work suggesting that three-frequency quasiperiodic attractors are common in typical dynamical systems.