摘要
研究了有界噪声激励下对称不连续系统的混沌动力学行为,将光滑系统中传统的Melnikov方法扩展到对称不连续系统中.首先假设未扰动系统是一个分段哈密尔顿系统,通过测量扰动系统稳定和不稳定流形之间的距离,得到随机Melnikov过程,然后建立统计意义下混沌发生的均方准则.结果表明,噪声强度的增强不仅会产生或加强系统混沌,还会抑制混沌,最后通过庞加莱映射与0-1测试的数值模拟验证了上述结果.
The effects of bounded noise excitation on the chaotic dynamic behavior of symmetric discontinuous systems are studied and the traditional Melnikov method in smooth systems is extended to symmetric discontinuous systems.Firstly,we assume that the undisturbed system is a piecewise Hamiltonian system,and the random Melnikov process is obtained by measuring the distance between the stable and the unstable manifolds of the disturbed system. Then the mean square criterion of chaos occurrence in the statistical sense is established. The results show that the enhancement of noise intensity not only generates or strengthens system chaos,but also suppresses chaos. Finally,the Poincarémap and numerical simulation of 0-1 test is used to verify validity of the mean square criterion.
作者
贺文娟
李晶
刘迪
HE Wenjuan;LI Jing;LIU Di(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China;School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China)
出处
《河南科学》
2020年第3期356-362,共7页
Henan Science
基金
国家自然科学基金(11402139)。
