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 \approx 0.9 ) and \ddot { \nu } < 0 ( r \approx 0.85 ) , and of \nu and \dot { \nu } ( r \approx 0.7 ) .
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 \approx 5 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 .