The method of multiple scales is used to determine the equations of modulation of amplitude and phase . the steady state response can be obtained by solving a couple of algebraic equations , which have been achieved by careful deduction under some conditions . and because of the complexity of the equations , programs are necessary to solve the equations mentioned above , and certain graphs are presented . based on chapter two , in chapter three , the method of multiple scales is introduced to the study of the multiple - dimensional nonlinear stochastic systems under random external excitation 在第二章基础上，第三章将多尺度法引入到相应的随机系统的研究中；严格推导了系统的约简方程，用矩方法求出稳态解应满足的方程，获得一些结果；并且数值模拟结果与理论推导的结果是一致的；并注意到，与其对应的确定性系统相比较，系统响应从周期解变为近似周期解，系统的相轨线从极限环变为扩大的近似极限环；随着激励带宽的增大，此扩大的近似极限环的宽度将增大。
It is well known that the absence of periodic or chaotic behavior , which guarantees complete stability , is a requirement for many applications . we call that a cnn is completely stable , if any initial condition ( except at most for a zero measure set ) bring the system to an equilibrium point 众所周知，在cnn的各种应用中，都要求系统不能存在周期轨道以及混沌吸引子，因此保证系统的稳定性则变得十分必要。所谓cnn的稳定性是指系统除了从一测度为零的集合为初始点出发的轨线外，其它的轨线最终都趋于某个稳定的平衡点。
Here these stability results do not require a lyapunov function to decrease along trajectories of the system , and we also do not give conditions on continuous portion or discrete portion of the systems respectively , but we can give mixing conditions on them to ensure that it does n ' t increase quickly 本文所用的lyapunov直接方法不同于以往的常规方法，主要表现在所找的lyapunov函数不再局限于沿系统轨线单调递减，也不再局限于对离散或连续部分分别设置条件，而是对其离散和连续部分设置混合条件以保证其不能增长太快
In the second chapter , we obtain the necessary and sufficient condition where the cubic kolmogorov type system is bounded if homogeneous polynomials of degree 3 are relatively prime . and we obtain there are only four behaviours of the trajectories near the equator of the bounded cubic system if the homogeneous polynomials of degree 3 are relatively prime . in the third chapter , we study the existence and nonexistence of limit cycle for a class of bounded cubic systems 第一章为引言；第二章，我们得到了齐三次项互素时三次kolmogorov型系统有界的充分必要条件及其在赤道上孤立奇点附近轨线的分布情况有且仅有四种；第三章，我们研究了一类有界三次kolmogorov型系统极限环的存在性与不存在性。
In the fourth part , by using the bifurcation theory of planar dynamical systems and the method of detection functions , the paper gives a configuration of limit cycles forming compound eyes . with the help of numerical analysis ( usi ng maple ) , it is shown that there exist parameter groups such that a z7 - equivariant planar polynomial vector field of degree 7 has at least 36 limit cycles with z7 - symmetry 然后，对于一组特定的参数值，研究了它的相轨线的变化趋势；第四部分指出：在一定的条件下，利用平面动力系统分支理论以及判定函数法，在计算机数学软件( maple )的帮助下，得到结论： 7次z _ 7 -等变平面向量场至少有36个极限环，形成具有z _ 7 ?对称性的极限环分布。
The results show that , when and 02 are in various intervals , the trajectories for systems ( i ) are either ultimately periodic or convergent to an equilibrium . the difference between system ( i ) and system ( ii ) only lies on the sign of self - feedback coefficient , but their asymptotic behavior of trajectories are much different . for the given initial value , the solutions for system ( ii ) all converge to the certain equilibrium 结果表明：当_ 1和_ 2在不同的取值范围内，系统( )的解或收敛到某一平衡点，或无限逼近于某个周期解，且部分_ 1 ， _ 2下的极限环全局稳定；系统( )与系统( )的区别仅在于自反馈系数的符号为负，但由此其解轨线的极限性态发生了很大的变化，对于确定的初值，系统( )的解均收敛到确定的平衡点。
Abstract : in this paper a new adaptive neural network controller is presented for a class of continuous - time nonlinear time delay systems subject to modeling uncertainty . the neural network model requires a priori knowledge about plant dynamics to provide prediction models for time delay systems . an adaptive controller based on neural networks was developed to produce the desired tracking performance in uncertain conditions . stability of the closed - loop system is proved by the lyapunov method . the effectiveness of the proposed scheme was demonstrated through its application to the control of a continuous stirred tank reactor 文摘:针对模型不确定性的连续时间时滞系统,提出了一种新的神经网络自适应控制.系统的辨识模型是由神经网络和系统的已知信息组合构成,在此基础上,建立时滞系统的预测模型.基于神经网络预测模型的自适应控制器能够实现期望轨线的跟踪,理论上证明了闭环系统的稳定性.连续搅拌釜式反应器仿真结果表明了该控制方案的有效性
It is usually deleterious when there appears chaos in the systems owing to chaos uncertainty , therefore , it is necessary to control chaos if chaos exists ; on the other hand , chaos contains much information , but the trajectory of chaos attractor is almost unstable , rapidly variational and hard to hold on . the saved information is easy to alternate , so it is unuseful unless chaos is under controlled . chaos control has attracted a great deal of attention from non - linear and this problem is also a complex problem of nonlinear 通常情况下，由于混沌的不确定性，系统中出现混沌是有害的，有必要在系统出现混沌时进行控制；而另一方面，混沌包含着极其丰富的信息，但是混沌奇怪吸引子内的轨线(或信息)是高度不稳定的，瞬息万变，难以捕捉，因此即使混沌信息存储下来，也会改变，往往难以重复识别，如不加以控制，根本无法应用。
Thirdly , the adaptive iterative learning control is used for the dynamics in the steady state optimization of nonlinear industrial process . the process operates continuously without resetting of initial value . the difficulty of selecting target trajectory is overcome effectively 第三，对非线性工业控制系统的稳态优化问题，用自适应迭代学习控制对其动态施行控制，不需要状态重置，系统是连续运行的，并且有效克服了ilc应用到稳态优化控制中目标轨线选取的困难。
Adaptive bounding technique is used to deal with unknown boundedness of approximation errors . the arbitrary output tracking accuracy is achieved by tuning the design parameters . thirdly , based on the results in chapter 3 , two design approaches of adaptive iterative learning control ( ailc ) are proposed for two classes of parametric nonlinear time - delay systems 神经网络用于逼近未知的非线性时滞函数，当状态不可测时，采用时滞滤波器估计系统状态，利用backstepping技术设计权值自适应律和控制律，占优化方法处理时滞基函数，自适应界化技术处理逼近误差的未知上界，通过调节设计参数可以实现对目标轨线任意精度的跟踪。
