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We model the evolution of spin frequency's second derivative $\ddot\nu$ andbraking index $n$ of radio pulsars with simulations within the phenomenologicalmodel of their surface magnetic field evolution, which contains a long-termdecay modulated by short-term oscillations. For the pulsar PSR B0329+54, themodel can reproduce the main characteristics of its $\ddot\nu$ variation withoscillation periods, predicts another $\sim 50$ yr oscillation component andanother recent swing of the sign of $\ddot\nu$. We show that the "averaged" $n$is different from the instantaneous $n$, and its oscillation magnitudedecreases abruptly as the time span increases, due to the "averaging" effect.The simulation predicted timing residuals agree with the main features of thereported data. We further perform Monte Carlo simulations for the distributionof the reported data in $|\ddot\nu|$ versus characteristic age $\tau_{\rm c}$diagram. The model with a power law index $\alpha=0.5$ can reproduce the slopeof the linear fit to pulsars' distributions in the diagrams of$\log|\ddot\nu|-\log\tau_{\rm c}$ and $\log|n|-\log\tau_{\rm c}$, but theoscillations are responsible for the almost equal number of positive andnegative values of $\ddot\nu$, in agreement with our previous analyticalstudies; an oscillation period of about several decades is also preferred.However the range of the oscillation amplitudes is $-11.4\lesssim\logf\lesssim-10.2$, slightly lager than the analytical prediction, $\logf\simeq-11.85$, because the "averaging" effect was not included previously.

Modeling the Evolution and Distribution of the Frequency's Second Derivative and Braking Index of Pulsar Spin with Simulations