带耦合项的含时受迫谐振子的量子特性

采用量子不变量理论,推导出带耦合项的含时受迫谐振子量子态的时间演化算符,结果表明系统会随时间演化到压缩态,并且计算了量子涨落和产生压缩的条件。     

关于二部图圈的一个注记

设G=（X,Y;E）是连通二部图,│X│= │Y│=n,则（1）NC2=n≥4,则G是点泛圈偶图。（2）NC2≥n-1≥4,且6≥2,则G含有Hamilton圈,或者G的任何一点都含在G中长为2n-2的圈中,且这个圈为G的控制圈。     

Chaotic Behavior of a Generalized Hamiltonian System and Its Circuit Implementation北大核心CSCD

A kind of generalized Hamiltonian systems with dissipative structure and external input is proposed. By configuring its structure matrix and external input, a simpler three-dimensional dynamical system with only one fixed point is designed to illustrate the existence of chaos. Useful tools, including phase portrait, Poincaré section, Lyapunov exponents, bifurcation diagram and power spectrum, are used for detecting chaotic behavior of the proposed system with the enhancement of DC input. Compared with the known three-dimensional chaotic systems, the proposed system has the following two characteristics: Its dissipativity is related to system state variables and its Lyapunov dimension is closer to 3. Finally, a circuit implementation of the new system is presented and the results recorded on an analogue oscilloscope further verify the existence of chaotic behavior. © 2017, The Journal of Agency of Complex Systems and Complexity Science. All right reserved.     

一类五次哈密顿系统在四次扰动下的极限环分支

运用判定函数方法,借助于数值计算方法研究了一类五次哈密顿系统在四次多项式扰动下的极限环分支情况,通过获得的判断曲线得出系统可以同时分支出6个极限环,而且6个极限环的情况有((3,0),3)和((0,3),3)两种分布形式.使用数值探测方法对所得结果进行了模拟检验, 给出了6个极限环的具体位置.而且研究了该系统在一些特殊扰动下的极限环数目及分布情况.