摘要
研究了 Duffing系统中作为倍周期分岔前兆的对称破缺分岔及其机理 ,Lyapunov指数与对称破缺分岔之间的关系 .研究表明对称破缺分岔意味着仅含奇次谐波周期解的失稳和稳定的含有奇、偶次谐波周期解的出现 ,而且在此临界稳定点应有最大 Lyapunov指数等于零 .通过数值计算发现 ,在达到倍周期分岔前最大 Lyapunov指数经历了 3个零点 ,对应于系统的两次对称破缺分岔和一次逆对称破缺分岔 ,并确定了分岔点的 f值 .
The mechanism of the symmetry breaking bifurcation, a prerequisite for period-doubling bifurcations, is presented. It is demonstrated that the symmetry breaking bifurcation is a bifurcation from a solution containing only odd harmonics to one containing both odd and even harmonics. The relationship between the maximum Lyapunov exponent and the symmetry breaking bifurcation is also investigated. The value of f at which the symmetry breaking occurs is determined through the computation of the zero maximum Lyapunov exponent. The numerical simulation shows that the maximal Lyapunov exponent experiences three zeros, corresponding to twice symmetry breaking bifurcations and once reverse symmetry breaking bifurcation.
出处
《武汉理工大学学报（交通科学与工程版）》
2005年第1期45-48,共4页
Journal of Wuhan University of Technology（Transportation Science & Engineering）
基金
"十五"国防预研项目资助 (批准号 :10 10 5 0 10 2 0 2 )
