【作者】 赵瑞芹；

【导师】 宋运忠；

【作者基本信息】 河南理工大学 ， 控制理论与控制工程， 2009， 硕士

【摘要】 由于动态共存吸引子Newton-Leipnik(N-L)系统,具有上下两个不同的奇异吸引子,所以它的动力学性质更为丰富,潜在应用价值更大。论文从动力学性质分析和电路实现两个方面对N-L系统进行了研究。理论分析方面,运用庞加莱截面、李亚普诺夫指数、李亚普诺夫维数及分岔图等工具对N-L系统进行了详细的探讨,并结合图形仿真和计算,进一步研究了N-L系统的动力学行为随参数变化的演化特性。电路实现方面,首先对N-L方程的状态变量进行比例压缩变换、微分-积分转换和时间尺度变换。其次根据变换后的方程设计出各模块电路,再将各模块按方程中各状态变量的对应关系联结起来。结果表明N-L方程由反相加法器、积分器、乘法器和反相器等常用器件即可实现,而且这种实现方式具有如下三方面优点:(1)模块化设计具有普适性,比较容易扩展到其它非线性系统;(2)由于采用了反相加法器,各个电路参数独立可调,互不影响,便于电路参数选择和调试;(3)混沌信号的频谱分布范围可由积分电阻或积分电容大小的改变来实现,便于实际应用。最后,通过EWB电路实现与MATLAB仿真结果的对比表明研究方案的合理性。更多还原

【Abstract】 Due to the dynamical co-existing attractor, the Newton-Leipnik (N-L) system has two different strange attractors, which may possess much more enriched dynamic properties and potential values. In this paper, dynamical analysis and circuit implementation of N-L system are addressed.As to theoretical analysis, Poincare section drawing, Lyapunov exponent computation, Lyapunov dimension calculation and bifurcation diagram drawing were borrowed, under auspices of graphic simulation and calculation, the character of dynamics evolution of the N-L system corresponding to parameter perturbation was investigated thoroughly.As to circuit implementation, variable-scale attenuation, differential to integral conversion and time-scale transform were executed to the N-L equation at first. Then, each module circuit was designed and linked with the other ones according to state variable couplings. And, going further, results demonstrate that the N-L system can be realized by Inverted Adders, Integrators, Inverters and the other easily obtained devices. Scheme supposed here outperforms the other ones in the following three points: (1) Modularization design is universal, and can be easily expanded to the other nonlinear systems. (2) The circuit parameters can be adjusted independently because of usage of Inverted Adder, so it’s convenient for parameter choice and debugging. (3) The chaotic signal spectrum distribution can be regulated by adjustment of the value of the Integral resistor or capacitance, which makes it liable for engineering application. Circuit implementation via EWB and simulation under MATLAB for the N-L system verify the efficacy of the put forward method.更多还原