0
2013
Impact Factor

    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 $\alpha_c = 1$.
    Keywords: Poincaré recurrence, Afraimovich–Pesin dimension, Fibonacci stairs, circle map, van der Pol oscillator
    Citation: Semenova N. I., Anishchenko V. S., Poincaré recurrences in a stroboscopic section of a nonautonomous van der Pol oscillator, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp.  149-156
    DOI:10.20537/nd1402002


    Download File
    PDF, 898.75 Kb




    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License