项目名称: 动力系统中随机共振及其在神经系统中的应用研究
项目编号: No.11202120
项目类型: 青年科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 宁丽娟
作者单位: 陕西师范大学
项目金额: 26万元
中文摘要: 噪声的出现使确定性系统出现极大的改变,甚至从根本上改变系统的性质。一方面,噪声能够消极地破坏序,导致均匀,起到破坏相变的作用。另一方面,噪声又能积极地与信号及系统取得最佳匹配,出现随机共振现象。考虑不同类型的噪声对动力系统的复杂而丰富的作用,以及实际系统的非对称性,研究非高斯噪声和信号共同作用下,粒子在各稳态间的运动,分析随着非高斯噪声的变化,系统输出的信噪比及粒子的定向输运;建立系统含时解的瞬态FPK方程,利用本征函数法分析系统的瞬态含时解,研究噪声对系统随时间演化行为的影响;利用平均法及指数关联函数公式,通过把高阶矩化为低阶矩,研究由乘性噪声、加性噪声及调制噪声共同驱动的线性系统中的随机共振,探索此系统中的相关参数及噪声对输出信噪比的影响;利用非线性动力学理论,研究FHN模型和IF模型在噪声扰动下的神经元系统的动力学行为及随机共振,分析噪声对改善某些神经功能病变的影响。
中文关键词: 随机共振;噪声;信噪比;神经系统;
英文摘要: The appearance of noise makes enormous change in the definite system, and it even fundamentally change the nature of system.On the one hand, noise can destroy the order negatively,resulting in uniform, and has a destructive action on phase transition. On the other hand, it can get the optimum matching with the signal and system actively, appearing stochastic resonance phenomenon.Considering the rich and complex effect of the different types of noise on the asymmetry of the actual system, the motion of particles between the steady states is researched under the interaction between non-Gaussian noise and signal,and in addition, the output signal-to-noise ratio and the transport of particle are discussed;On the basis of builting the FPK equation with transient solution of time and using eign function approach, the effect of noise on the evolution behavior of the system with time is researched; Using the method of average and the formula of exponential correlation, by lowering order stochastic resonance is investigated in a linear system driven by multiplicative, additive noise and signal modulated noise, we explore the effect of the related parameters and noise in the system on the output signal-to-noise ratio ;In FHN model and IF model, dynamical behavior of the neuron system and stochastic resonance are research
英文关键词: Stochastic resoance;Noise;Signal-to-noise ratio;Nervous system;