研究关联噪声与周期信号共同激励下周期势系统的动力学特性.首先利用统一色噪声近似的方法,将二维马尔可夫过程简化为一维非马尔可夫过程,得到了周期势系统的Fokker-Planck(FPK)方程;然后在理论上推导出系统的准稳态概率密度函数(quasi-...研究关联噪声与周期信号共同激励下周期势系统的动力学特性.首先利用统一色噪声近似的方法,将二维马尔可夫过程简化为一维非马尔可夫过程,得到了周期势系统的Fokker-Planck(FPK)方程;然后在理论上推导出系统的准稳态概率密度函数(quasi-steady-state probability density,简称QSPD)的表达式;最后进一步运用4阶龙格库塔算法对QSPD进行数值模拟,分析了噪声及系统各参数对该周期势系统QSPD的影响.展开更多
The mathematical topological rule was applied to plot the predominance area diagram.Based on the analysis of the mutually conjugated,only two diagrams were the best topological embryonic graphs to build the predominan...The mathematical topological rule was applied to plot the predominance area diagram.Based on the analysis of the mutually conjugated,only two diagrams were the best topological embryonic graphs to build the predominance area diagram of Me-S-O system.Combined with topological rules and thermodynamic calculation,four relation-diagrams were denoted asαandβstable and unstable plane-topological diagrams,which were plotted for the Pb-S-O system and Zn-S-O system.The results show thatβstable plane-topological diagram of Pb-S-O system andαstable one of Zn-S-O system are in accordance with the traditional predominance area diagram,which indicates that it is feasible to plot the predominance area diagram based on mathematical topological rules.Meanwhile,αunstable plane-topological diagram of Pb-S-O system can elucidate the phenomenon that metallic lead exists in higher oxygen and sulfur pressure area in modern bath smelting furnace.The mathematical topological rules broaden the application scope of the predominance area diagram and enrich the practice of its plotting.展开更多
文摘研究关联噪声与周期信号共同激励下周期势系统的动力学特性.首先利用统一色噪声近似的方法,将二维马尔可夫过程简化为一维非马尔可夫过程,得到了周期势系统的Fokker-Planck(FPK)方程;然后在理论上推导出系统的准稳态概率密度函数(quasi-steady-state probability density,简称QSPD)的表达式;最后进一步运用4阶龙格库塔算法对QSPD进行数值模拟,分析了噪声及系统各参数对该周期势系统QSPD的影响.
基金Project(2011AA061003) supported by the High-Tech Research and Development Program of China
文摘The mathematical topological rule was applied to plot the predominance area diagram.Based on the analysis of the mutually conjugated,only two diagrams were the best topological embryonic graphs to build the predominance area diagram of Me-S-O system.Combined with topological rules and thermodynamic calculation,four relation-diagrams were denoted asαandβstable and unstable plane-topological diagrams,which were plotted for the Pb-S-O system and Zn-S-O system.The results show thatβstable plane-topological diagram of Pb-S-O system andαstable one of Zn-S-O system are in accordance with the traditional predominance area diagram,which indicates that it is feasible to plot the predominance area diagram based on mathematical topological rules.Meanwhile,αunstable plane-topological diagram of Pb-S-O system can elucidate the phenomenon that metallic lead exists in higher oxygen and sulfur pressure area in modern bath smelting furnace.The mathematical topological rules broaden the application scope of the predominance area diagram and enrich the practice of its plotting.
