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Eight pulsars have low braking indices, which challenge the magnetic dipolebraking of pulsars. 222 pulsars and 15 magnetars have abnormal distribution offrequency second derivatives, which also make contradiction with classicalunderstanding. How neutron star magnetospheric activities affect these twophenomena are investigated by using the wind braking model of pulsars. It isbased on the observational evidence that pulsar timing is correlated withemission and both aspects reflect the magnetospheric activities. Fluctuationsare unavoidable for a physical neutron star magnetosphere. Young pulsars havemeaningful braking indices, while old pulsars' and magnetars' fluctuation itemdominates their frequency second derivatives. It can explain both the brakingindex and frequency second derivative of pulsars uniformly. The braking indicesof eight pulsars are the combined effect of magnetic dipole radiation andparticle wind. During the life time of a pulsar, its braking index will evolvefrom three to one. Pulsars with low braking index may put strong constraint onthe particle acceleration process in the neutron star magnetosphere. The effectof pulsar death should be considered during the long term rotational evolutionof pulsars. An equation like the Langevin equation for Brownian motion wasderived for pulsar spin-down. The fluctuation in the neutron star magnetospherecan be either periodic or random, which result in anomalous frequency secondderivative and they have similar results. The magnetospheric activities ofmagnetars are always stronger than those of normal pulsars.

Fluctuating neutron star magnetosphere: braking indices of eight pulsars, frequency second derivatives of 222 pulsars and 15 magnetars