Cyclic evolution of radio pulsars on the time scale of hundreds of years

The recent massive measurements of pulsar frequency second derivatives have shown that they are 100-1000 times larger than expected for standard pulsar slowdown low. Moreover, the second derivatives as well as braking indices are even negative for about half of pulsars. We explain these paradoxical results on the basis of the statistical analysis of the rotational parameters $\nu$, $\dot \nu$ and $\ddot \nu$ of the subset of 295 pulsars taken mostly from the ATNF database. We have found strong correlation of $\ddot \nu$ and $\dot \nu$ either for $\ddot\nu > 0$ (correlation coefficient $r\approx0.9$) and $\ddot\nu < 0$ ($r\approx0.85$), and of $\nu$ and $\dot\nu$ ($r\approx0.7$). We interpret these dependencies as evolutionary ones due to $\dot\nu$ being nearly proportional to characteristic age $\tau_{ch}$. The derived statistical relations as well as "anomalous" values of $\ddot\nu$ are well explained in the framework of the simple model of cyclic evolution of the rotational frequency of the pulsars. It combines the secular change of $\nu_{tr}(t)$, $\dot\nu_{tr}(t)$ and $\ddot\nu_{tr}(t)$ according to the power law with $n\approx5$ and harmonic oscillations of 100--1000 years period with an amplitude from $10^{-3}$ Hz for young pulsars to $10^{-10}$ Hz for elder ones. The physical nature of these cyclic variations of the rotational frequency may be similar to the well-known red timing noise, however, with much larger characteristic time scale.