Atangana-Baleanu分数阶双稳系统的随机共振现象

Stochastic Resonance Phenomenon of Atangana-Baleanu Fractional Bistable System

针对基于常用分数阶微积分对随机共振现象的研究存在奇异性的问题,提出了基于Atangana-Baleanu分数阶微积分的双稳系统随机共振现象的研究方法。首先,根据Atangana-Baleanu分数阶微积分的定义构造了用于描述随机共振系统的Langevin方程;其次,通过改进的Oustaloup算法对其近似化求解;最后,编写仿真程序,利用控制单一变量法研究参数变化对随机共振的影响。仿真结果表明:噪声强度一定时改变分数阶求导阶次,分数阶求导阶次与输出信号的功率谱值呈非线性关系且存在一个最佳分数阶求导阶次使系统产生随机共振;分数阶求导阶次一定时改变噪声强度,噪声强度与输出信号的功率谱值呈非线性关系且存在一个最佳噪声强度使系统产生随机共振。

Aiming at the problem of singularity in the study of stochastic resonance based on commonly used fractional calculus,a research method of stochastic resonance in bistable systems based on Atangana-Baleanu fractional calculus is proposed. First,according to the definition of Atangana-Baleanu fractional calculus,the Langevin equation is constructed to describe the stochastic resonance system. Second,it is approximated by the improved Oustaloup algorithm. Finally,simulation program is written to study the effect of parameter changes on stochastic resonance using the single variable control method. The simulation results show that when the noise intensity is constant,by changing the fractional order derivative order,there is a nonlinear relation between the order of fractional derivative and the power spectrum of the output signal and there is an optimal order of fractional derivative to generate stochastic resonance. When the order of fractional derivative is constant,by changing the noise intensity,there is a nonlinear relation between the noise intensity and the power spectrum value of the output signal and there is an optimal noise intensity to generate stochastic resonance.