混频产生混沌

几个频率不同的谐波成份在非线性器件的混合称为混频。用非线性微分方程描写混频电路的动态过程,一般都能根据电路定律表达出来。然而微分方程的解析表达式却大多求不出来,因而近代非线性科学的发展,用数值仿真求出微分方程的图形解。用一条空间曲线表示三个变量间的相互函数关系,并以此作为方程的求解结果。由数值仿真画出的空间曲线称为相图,其性状随激励源参数的不同而变化,混频可能出现周期态与混沌态两种振荡性状。在仿真的时间间隔内,周期态能明显画出一个闭合的周期轨,这个闭合轨可以是单循环或多循环的。混沌态的相图要比周期态复杂得多,如果在访真间隔内轨线最后无法完成闭合,说明这是非周期的混沌。

The Chaos Produced by Mixing

It is called mixing that the several harmonic component with different frequency is mixed in the nonlinear device .The dynamic process of the mixing circuits is described by the nonlinear differential equation which usually can be written by circuit law. However the analytical expression cannot mostly be found by the differential equation . Therefore in the development of modern nonlinear science, the graphical solutions of the differential equation are found by numerical simulation, the functional relation among three variation is expressed by a space curve, moreover the graphical solution is considered as the result of solving equations. The space curve plotted by numerical simulation is called phase portrait. Its shape and property vary with the parameter of excited source. The mixing may arise two sorts of oscillation pattern, the periodic and chaotic state .The periodic state can obviously obtain a closed period orbit in the simulation interval, the closed orbit may be single circle or multi- circle. The phase portrait of chaotic state is much more complex than the periodic state, it cannot display the close of trajectory in the simulation interval finally, therefore it is considered as chaos of non-periodic.