Chaos Structured by Mixing of Multi-Excited Source
Abstract: The solutions of dynamical system expressed with nonlinear differential equation usually is shown by using time function u(t). But this is not unique mode, when particularly u(t) cannot be solved. In the modern theory of circuit and system, we can select three dynamical variables in the nonlinear system to constitute 3-dimension phase space. The mutual nonlinear relation among three dynamical variables can be described by a bounded space curve. This is 3-dimension phase portrait. The nonlinear dynamical systems of regarding N>3 variation may constitute -dimension Euclidean space. The bounded space curve cannot be represented by concretely explicit parametric form in math. It cannot be solved analytically by human. However, the graphic solution can be plotted by numerical simulation. If the bounded space curve is non-periodic in simulation interval, this is orbital chaos of continuous time system. This paper researches the produce and property of chaos by means of the analysis method of frequency domain and theorem of power balance. We prove that the second order differential circuit which is constituted by mixing of multi-excited source with different frequency also can produce chaos.
文章引用: 黄炳华 , 梁永清 , 韦忠海 (2014) 多激励源混频构成的混沌。 现代物理， 4， 147-159. doi: 10.12677/MP.2014.46016
 Huang, B.H., Wei, Y.F. and Huang, Y. (2014) Describing chaos of continuous time system using bounded space curve. Journal of Modern Physics, 5, 1489-1501.
 黄炳华, 刘慧杰, 梁永清 (2014) 一阶微分电路构成的混沌. 现代物理, 4, 86-99.
 Huang, B.H., Li, G.M. and Liu, H.J. (2014) Power balance theorem of frequency domain and its application. Journal of Modern Physics, 5, 1097-1108.
 Huang, B.H. and He, X.Y. (2014) Power balance of multi-harmonic components in nonlinear network. Journal of Modern Physics, 5, 1321-1331.
 黄炳华, 李广明, 卫雅芬 (2012) 用虚功平衡原理求解无损耗系统的主谐波. 现代物理, 2, 60-69.
 黄炳华, 李广明, 刘慧杰 (2013) 由无损耗电路构成的非周期振荡. 现代物理, 1, 1-8.
 冯久超, 李广明 (2012) 功率平衡理论在研究非线性电路与混沌中的进展. 华南理工大学学报, 11, 13-18.
 梁永清, 黄炳华 (2014) 非线性电路频域的功率平衡. 太原理工大学学报, 3, 328-333.
 Huang, B.H., Huang, X.M. and Li, H. (2011) Main components of harmonic solutions of nonlinear oscillations. Procedia Engineering, 16, 325-332.
 Huang, B.-H., Yang, G.S., Wei, Y.F. and Huang, Y. (2013) Harmonic analysis method based on power balance. Applied Mechanics and Materials, 325-326; Manufacturing Engineering and Process II, 1508-1514
 黄炳华, 钮利荣, 蔺兰峰, 孙春妹 (2007) 功率平衡基础上的基波分析法. 电子学报, 10, 1994-1998.
 黄炳华, 黄新民, 韦善革 (2008) 用基波平衡原理分析非线性振荡与混沌. 通信学报, 1, 65-70
 Yu, S.M., Qiu, S.-S. and Lin, Q.H. (2003) New results of study on generating multiple-scroll chaotic attractors. Science in China (Series F), 46, 104-115.
 王兴元, 王明军 (2007) 超混沌Lorenz系统. 物理学报, 9, 5136-5141.