摘要
基于9阶van der Pol方程的分岔结果,设计了1个平衡点和2个极限环共存的三稳态电路.利用平均法分析了9阶van der Pol方程的分岔性质,设计了能够实现三稳态现象的无量纲方程的系统参数.根据基尔霍夫电路定理,利用运算放大器和模拟乘法器等元件,构建了9阶van der Pol方程的电路原理图,并通过PSpice仿真和硬件电路试验验证了该电路的可行性和可靠性.试验结果表明,该电路系统中有1个稳定平衡点与2个稳定极限环共存的现象,为研究确定性激励以及随机激励下三稳态系统的动力学行为奠定了基础.
A kind of tri-stable circuit with one stable equilibrium point and two stable limit cycles was designed based on the bifurcation analysis of the ninth-order van der Pol equation. By using the averaging method,the bifurcation properties of the ninth-order van der Pol equation were analyzed,and the dimensionlessequation parameters which could achieve the tri-stable phenomena were designed. According to Kirchhoff laws,the circuit diagram of the ninth-order van der Pol equation was constructed with such elements as operational amplifiers,analog multiplier,etc. The feasibility and reliability of the circuit were verified by PSpice simulation and hardware experiments. The resultsshow that the proposed circuit system does have one stable equilibrium point and two stable limit cycles,which laysa foundation for further study on the dynamic behaviors of tri-stable system under deterministic excitation and random excitation.
出处
《天津大学学报(自然科学与工程技术版)》
EI
CSCD
北大核心
2016年第7期709-715,共7页
Journal of Tianjin University:Science and Technology
基金
国家自然科学基金资助项目(11372211)