有界噪声激励下Josephson系统的混沌运动

Chaotic motion of a Josephson system excited by bounded noise

利用随机Melnikov方法分析了有界噪声激励下Josephson系统的运动,并运用均方准则得到了系统产生混沌的临界值。结果表明:有界噪声对系统混沌行为的产生起到了加速的作用;且有界噪声的强度越大,混沌吸引子的发散程度就越大。最后利用数值模拟得到系统的庞加莱映射,分析了在不同参数组合下系统庞加莱映射的特征。结果显示:当有界噪声中的一个参数发生改变,系统的庞加莱映射也会发生相应的改变;特别是有界噪声的激励强度增大时,系统庞加莱映射的发散程度也会随之增大。这从侧面验证了理论结果的正确性。

The chaotic behavior of Josephson system under bounded noise is discussed.Firstly,the motion of Josephson system under bounded noise is investigated by employing stochastic Melnikov technique,and the necessary conditions for chaotic motion of this stochastic system are provided according to the mean square criterion.It is found that the bounded noise speeds up the chaotic motion of the stochastic system,and the bigger the bounded noise intensity is,the greater the chaotic attractor spreads.Finally,the Poincare map of the Josephson system under bounded noise is investigated numerically,and the features of Poincare maps under different parameter combination are analyzed.The results obtained show that the Poincare map of the system changes as the parameter of bounded noise changes,especially the intensity of bounded noise increases,then the divergence of the Poincare map of the system will increase which verifies the theoretical results obtained.