非线性分数阶双稳系统逻辑随机共振的研究

Logic Stochastic Resonance Induced by a Nonlinear Fractional Bistable System

在整数阶逻辑随机共振的郎之万方程基础上构建了分数阶情况下的郎之万方程。对该方程描述的非线性分数阶双稳系统进行了仿真验证,分析分数阶阶次和系统参数的改变对逻辑随机共振现象的影响。结果表明当分数阶阶次小于临界值时,即使没有外加高斯白噪声或微弱周期信号也能观察到逻辑随机共振现象;当分数阶阶次大于临界值时,需要外加高斯白噪声或微弱周期信号才能实现逻辑随机共振,选择合适的噪声强度、微弱周期信号振幅、频率等可以提高逻辑输出的成功率。

Based on the logic stochastic resonance of integer-order Langevin equation, a fractional-order Langevin equation is constructed. A simulation verification for the nonlinear fractional bistable system based on this equation is carried out, and the impact on logic stochastic resonance phenomenon when changing fractional order and system parameters is analyzed. The results show that when the fractional order is less than the critical value, even if no additional Gaussian white noise or weak periodic signal the logical stochastic resonance phenomenon can be observed; when the fractional order is greater than the critical value, the additional Gaussian white noise or weak periodic signal is necessary in order to achieve logical stochastic resonance, the success rate of logical output can be increased by selecting appropriate noise intensity, amplitude and frequency of weak periodic signal.