参量激励下的Duffing-van der Pol系统是一个多参数的非线性系统，本文研究了该系统的二参数共振分叉问题，利用多尺度方法得到了系统的一次近似平均方程和分叉响应方程，分析了分叉方程的解及其在二分叉参数平面上的分布，研究了零解...参量激励下的Duffing-van der Pol系统是一个多参数的非线性系统，本文研究了该系统的二参数共振分叉问题，利用多尺度方法得到了系统的一次近似平均方程和分叉响应方程，分析了分叉方程的解及其在二分叉参数平面上的分布，研究了零解的稳定性。展开更多
A DC DC buck converter c on trolled by naturally sampled, constant frequency PWM is considered. The existe nce of chaotic solutions and the output performance of the system under differen t circuit parameters are s...A DC DC buck converter c on trolled by naturally sampled, constant frequency PWM is considered. The existe nce of chaotic solutions and the output performance of the system under differen t circuit parameters are studied. The transforming pattern of system behavior fr om steady state to chaotic is discovered by the cascades of period doubling bi furcation and the cascades of periodic orbit in V I phase space. Accordingl y, it is validated that change of values of the circuit parameters may lead DC DC converter to chaotic motion. Performances of the output ripples fro m steady state to chaotic are analyzed in time and frequency domains respective ly. Some important conclusions are helpful for opt imization design of DC DC converter.展开更多
Catalytic CO oxidation on platinum group metals exhibits nonlinear phenomena such as hysteresis and bifurcation.Elucidation of the nonlinear mechanisms is important for catalyst design and control of reaction routes.P...Catalytic CO oxidation on platinum group metals exhibits nonlinear phenomena such as hysteresis and bifurcation.Elucidation of the nonlinear mechanisms is important for catalyst design and control of reaction routes.Previous studies have offered initial insights into the local bifurcation behavior of CO oxidation.However,since the bifurcation behavior of CO oxidation is determined by multiple parameters such as temperature,total flux,and CO fraction,it is difficult to predict the global bifurcation behavior in the resulting high-dimensional parameter space.It is for this reason that the observed nonlinear phenomena reflect just the local bifurcation features of CO oxidation.In this paper,an elementary chemical law(topological invariance) concerning the bifurcation behavior of CO oxidation on platinum group metals such as Pd(111) is found from a topological perspective.Following the elementary law,we put forward a topological approach to model the critical criteria for the reaction hysteresis and bifurcation.The model may be applied to predict the global bifurcation behavior of CO oxidation in the high-dimensional parameter space.The topological approach and the model results may be useful as a guide in thinking about the complex reaction mechanism,designing reaction routes,and actively controlling the bifurcation behavior of the CO oxidation reaction.展开更多
文摘A DC DC buck converter c on trolled by naturally sampled, constant frequency PWM is considered. The existe nce of chaotic solutions and the output performance of the system under differen t circuit parameters are studied. The transforming pattern of system behavior fr om steady state to chaotic is discovered by the cascades of period doubling bi furcation and the cascades of periodic orbit in V I phase space. Accordingl y, it is validated that change of values of the circuit parameters may lead DC DC converter to chaotic motion. Performances of the output ripples fro m steady state to chaotic are analyzed in time and frequency domains respective ly. Some important conclusions are helpful for opt imization design of DC DC converter.
基金supported by the National Natural Science Funds for Distinguished Young Scholars (50925625)the National Natural Science Foundation of China (50906015)
文摘Catalytic CO oxidation on platinum group metals exhibits nonlinear phenomena such as hysteresis and bifurcation.Elucidation of the nonlinear mechanisms is important for catalyst design and control of reaction routes.Previous studies have offered initial insights into the local bifurcation behavior of CO oxidation.However,since the bifurcation behavior of CO oxidation is determined by multiple parameters such as temperature,total flux,and CO fraction,it is difficult to predict the global bifurcation behavior in the resulting high-dimensional parameter space.It is for this reason that the observed nonlinear phenomena reflect just the local bifurcation features of CO oxidation.In this paper,an elementary chemical law(topological invariance) concerning the bifurcation behavior of CO oxidation on platinum group metals such as Pd(111) is found from a topological perspective.Following the elementary law,we put forward a topological approach to model the critical criteria for the reaction hysteresis and bifurcation.The model may be applied to predict the global bifurcation behavior of CO oxidation in the high-dimensional parameter space.The topological approach and the model results may be useful as a guide in thinking about the complex reaction mechanism,designing reaction routes,and actively controlling the bifurcation behavior of the CO oxidation reaction.
