Poincaré recurrences in a stroboscopic section of a nonautonomous van der Pol oscillator
2014, Vol. 10, No. 2, pp. 149-156
Author(s): Semenova N. I., Anishchenko V. S.
In the present work we analyze the statistics of a set that is obtained by calculating a stroboscopic section of phase trajectories in a harmonically driven van der Pol oscillator. It is shown that this set is similar to a linear shift on a circle with an irrational rotation number, which is defined as the detuning between the external and natural frequencies. The dependence of minimal return times on the size ε of the return interval is studied experimentally for the golden ratio. Furthermore, it is also found that in this case, the value of the Afraimovich–Pesin dimension is $\alpha_c = 1$.
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