时空噪声激励下可激发系统的随机响应及应用研究

项目名称： 时空噪声激励下可激发系统的随机响应及应用研究

项目编号： No.11302169

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 都琳

作者单位： 西北工业大学

项目金额： 25万元

中文摘要： 可激发系统作为反应扩散系统的一种，其动力学研究是当今学术界的热点。目前的研究主要集中于局部反应过程，而忽略空间扩散的作用，涉及随机因素的研究更不多见。本项目将围绕随机可激发系统的两个核心问题-随机响应和随机控制展开应用基础研究，构建适用于随机可激发系统的理论分析方法和控制策略，揭示时空噪声对系统稳态响应的影响，阐明利用随机信号抑制螺旋波和时空混沌的物理机制。研究内容包括：通过随波坐标系变换，研究时空白噪声激励下的模式振幅方程，得到振幅响应的精确平稳解；利用非线性拟谱方法，将时空关联噪声转化为白噪声谱。通过空间离散化，结合随机平均法，建立和求解系统近似响应的FPK方程，探索噪声诱导的随机分岔和跳变现象；以降低振幅的尾部概率密度为目标，设计和发展多层耦合可激发系统的随机控制策略。本项目的研究将拓展随机动力学的理论框架，丰富可激发系统的研究成果，为心脏震颤的预防和治疗提供理论依据。

中文关键词： 可激发系统；时空噪声；随机响应；随机分岔；控制策略

英文摘要： As a kind of reaction diffusion systems, the research on the dynamics of excitable systems has become one of hot topics in current academic community. Recent studies mainly focus on the local reaction process, ignoring the effect of space diffusion and random factors. This program will develop applied basic research around two fundamental issues of stochastic excitable systems: stochastic response and stochastic control. The theoretic analytic method and control strategy of stochastic excitable systems will be established, to explore the effect of spatial-temporal noise on stable responses. The physical mechanism of supressing spiral wave and spatiotemperal chaos by noise signals will also be illustrated. The research contents include as follows. Based on transformation of wave coordinates, the model equation of amplitude driven by white noise is investigated, and thus the exact stable solution of amplitude responses is obtained. Using nonlinear pseudo-spectral method, the noise with spatial-temporal correlation is converted to white noise spectrum. By spatial discretization, combined with stochastic average method, the FPK equation of approximate responses is established and solved, to explore noise induced phenomena of stochastic bifurcation and jumping. Aiming to decrease the tail probability desity of the am

英文关键词： Excitable system；Spatial-temporal noise；Stochastic response；Stochastic bifurcation；Control strategy