脉冲星自转的稳定性是其最显著的特征，使得我们可以利用这种特征确定双星轨道的形状和尺度，提供计时标准，研究强引力场中的广义相对论效应，检验引力波，探测太阳系外行星。通过磁偶极辐射的自转减慢力矩，脉冲星的角动量会发生变化，所以对于脉冲的时间到达的影响通常是可以预测的。然而，在脉冲星自转中两种有趣的不规则性被观测到，它们分别是：“跃变”，表现多为自转速率的突然增加，并伴随长期的恢复过程；“计时噪声”，表现多为相当连续不稳定的行为，并且多由低频结构组成。对于计时噪声更加全面的理解会有助于我们深入了解中子星的内部结构。我们尝试解释普遍存在于脉冲星计时残差中的一些现象：脉冲星自转频率二阶导数存在正负问题，一些残差中的复杂结构不能单纯地由传统时间拟合中的立方项所解释，以及对于给定单个脉冲星的计时残差结构会随着数据段时间跨度的变化而改变。我们的样本来自于Hobbs等人在2010年发布的数据，其中的计时残差是扣除了自转频率以及其一阶导数后得到的。我们首先基于¨ν的符号将残存分为不同的模式，然后我们使用张双南和谢祎提出的磁场振荡模型，通过马尔科夫链蒙特卡洛的方法拟合不同类型的残差并获取其最佳拟合参数。最后，我们模拟具有典型参数的单个脉冲星20 yr的演化，并采用传统的计时拟合方法对其数据加以分析。通过选择模拟数据的不同数据跨度，我们发现大部分观测的计时残差类型可以被很好的重现，这也是首次观测的残差被一个采用很少参数的模型所拟合并重现出来。对于不同残差模式在P−˙P图上的分布，我们认为：(1) 单磁场振荡模式普遍存在于脉冲星的整个演化过程中。(2) 在脉冲星的演化过程中，可能存在一个转换区域使得磁场的多振荡模式得以存在。我们进一步推断这种转换是由影响计时残差行为的不同尺度的霍尔波所引发。此外，我们还做了一些关于脉冲星其它方面的研究，包括经典跃变和慢跃变对于普遍计时残差的影响，磁倾角的演化问题以及脉冲星星族合成。

The most remarkable feature of pulsars is their rotational stability, which enables us to de-termine the shapes and sizes of their binary orbits, to provide the time standard, to study generalrelativistic effects in strong gravitational fields, to test gravitational waves, and also to detect exo-planets. The angular momentum of a pulsar changes through the braking torque of the magneticdipole radiation; therefore, the effect on the pulse times of arrival is usually predictable. Howev-er, two interesting irregularities in pulsar rotation have been observed: namely ‘glitches’ whichare sudden increases in their rotation rate followed by a period of relaxation, and ‘timing noise’which is a fairly continuous erratic behaviour and consists of low-frequency structures. A morecomplete understanding of pulsar timing noise will provide us an insight into the interior structureof neutron stars.We try to explain some phenomena existing generally in the timing residuals: the sign ofthe second derivative of pulsar’s spin-frequency (¨ ν), some sophisticated structures that cannot beexplained simply by the cubic polynomial in the conventional timing solution fitting, and the struc-ture of timing residuals of a given pulsar changes depending on the time span of data segments.The sample is taken from Hobbs et al. (2010), in which the pulsar’s spin-frequency and its firstderivative have been subtracted from the timing solution fitting. We first classify the timing resid-ual patterns into different types based on the sign of ¨ν. Then we use the magnetic field oscillationmodel developed in our group to fit the different kinds of timing residuals with the Markov ChainMonte Carlo method and find good match with the data. Finally, we simulate the spin evolutionover 20 years for a given pulsar with typical parameters and analyze the data with the conven-tional timing solution fitting. By choosing different segments of the simulated data, we find that most of the observed residual patterns can be reproduced successfully. This is the first time thatthe observed residual patterns are fitted by a model and reproduced by simulations with very fewparameters. From the distribution of the different residual patterns in theP−˙Pdiagram, we arguethat (1) a single magnetic field oscillation mode exists commonly in all pulsars throughout their lifetimes; (2) there may be a transition region over the lifetimes of pulsars, in which multiple mag-netic field oscillation modes exist. We further speculate that the transition may be triggered byHall waves of different scales, which influence the behavior of timing residuals.Moreover, we also do some other research about pulsars, including the influence of the classicglitches and slow glitches to the general timing residuals, the evolution of the magnetic inclinationangle and population synthesis.