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研究了高斯色噪声和周期信号共同作用下非对称双稳耦合网络系统的协同效应. 此系统是由大量振荡器组成的网络模型, 个体与个体之间的相互运作、变化产生出复杂的非线性行为模式. 为了进行深入研究, 首先, 运用平均场理论、统一色噪声近似理论和等效非线性化等方法对原始
$ N $ 维系统进行降维近似. 其次, 借助役使原理得到简化模型的郎之万方程, 进一步根据两态模型理论推导出信噪比的理论表达式, 基于此发现系统产生了尺度随机共振现象. 最后, 分析了高斯色噪声、系统参数和周期信号等对非对称耦合网络系统随机共振行为的影响. 结果表明, 高斯色噪声自关联时间和噪声强度的增大, 能够促进尺度随机共振现象; 选取合适的耦合系数能使系统随机共振效应达到最佳. 此外, 还比较了高斯色噪声和高斯白噪声分别驱动下系统的随机共振问题, 发现高斯色噪声更有利于增强随机共振现象.-
关键词:
- 随机共振/
- 非对称双稳耦合网络系统/
- 信噪比/
- 高斯色噪声
In this work studied is the synergistic effect of asymmetric bistable coupled network systems under the action of Gaussian colored noise and periodic signal. The system is a network model consisting of a large number of oscillators. The interaction and change between individuals produce complex nonlinear behavior patterns. For further research, firstly, the original N-dimensional system is reduced and approximated by using the mean field theory, the unified colored noise approximation theory and the equivalent nonlinearization method. Secondly, the Langevin equation of simplified model is obtained through the slaving principle by using the two-state model theory to derive the theoretical expression of signal-to-noise ratio. It is found that the system produces the phenomenon of scale stochastic resonance. Finally, the effects of Gaussian color noise parameters, system parameters and periodic signal parameters on the stochastic resonance behavior of asymmetric coupled network systems are discussed. The results show that the increase of Gaussian colored noise correlation time and noise intensity can promote the scale stochastic resonance phenomenon; selecting appropriate coupling coefficient can achieve the optimal stochastic resonance effect. And the stochastic resonance phenomenon of the system driven by the Gaussian colored noise and the Gaussian white noise, respectively, are analyzed and compared with each other. Research result shows that Gaussian colored noise is more conducive to enhancing stochastic resonance phenomenon.-
Keywords:
- stochastic resonance/
- asymmetric bistable coupled network systems/
- signal-to-noise ratio/
- Gaussian colored noise
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