基于统计复杂度的非对称双稳系统的动力学复杂性研究

Dynamical complexity in an asymmetric bistable system via statistical complexity measures

本文运用统计复杂度和标准Shannon熵研究了乘性色噪声和加性白噪声共同作用下非对称双稳系统的动力学复杂性.考虑到系统势函数的非对称性,借助于Bandt-Pompe算法分别计算了系统总的以及左、右势阱的统计复杂度和标准Shannon熵,并在此基础上详细讨论了势阱的非对称性、加性白噪声、乘性色噪声及周期信号等对系统动力学复杂性的影响.结果表明,当这些因素变化时,系统总的统计复杂度和标准Shannon熵与系统单个势阱中的统计复杂度和标准Shannon熵呈现出明显不同的趋势,反映了其动力学复杂性的不同.

The dynamical complexity is quantified by the statistical complexity and the normalized Shannon entropy in an asymmetric bistable system subject to multiplicative colored and additive white noises. The total statistical complexity and the total normalized Shannon entropy of the system are calculated based on Bandt-Pompe methodology. Because of the asymmetry of the potential, the statistical complexity and the normalized Shannon entropy in two different potential wells of the system are also obtained, respectively. Then, the effects of potential asymmetry, additive white and multiplicative colored noises and periodic signal on the dynamical complexity of the system are discussed in detail. It can be seen from the results that the trends of the curves of the statistical complexity and the normalized Shannon entropy of the system are different from those of two potential wells of the system when changing the parameters of the system.