斜拉索主参数共振的稳定性分析

研究轴向激励下斜拉索的主参数共振的稳定性问题．考虑拉索垂度和几何非线性的影响,导出了拉索在轴向激励下的非线性参数振动方程．利用多尺度方法研究了斜拉索的主参数共振问题,并对其稳态解的稳定性作了较详细的分析．对斜拉索的主参数共振进行了数值模拟,得到了不同阻尼、初始条件及激励幅值作用下拉索的时程曲线．结果表明：斜拉索的固有频率与外激励参数对斜拉索稳态解的个数及其稳定性都存在直接影响,从而对斜拉索的参数设计起到了指导作用．     

一类两自由度含间隙系统的Hopf分岔

建立了一类两自由度含间隙系统的力学模型,并研究了该系统的周期运动及运动的受扰运动．通过选取适当的Poincare截面及系统碰撞的周期性条件,建立了系统的Poincare映射．利用Poincare映射数值证明了Hopf圈的存在性,揭示了并讨论了随着参数的变化系统通过Hopf分岔及周期倍化分岔向混沌演化的过程．最后讨论了系统参数对系统动力学行为的影响,为系统的动力学优化设计找到了理论依据．     

冲击式振动落砂机的动态响应与分叉

本文考虑一类振动落砂机简化力学模型的次谐运动、稳定性与分叉问题.数值工作表明该模型存在"跳跃"和多种分叉现象.     

基于CATIA二次开发的月牙肋钢岔管辅助设计系统开发与应用

利用自动化对象编程,针对水电站月牙肋钢岔管设计繁琐、工作量大、有限元计算前处理耗时长的缺点,开发出基于CATIA二次开发的辅助设计系统.该系统实现了月牙肋钢岔管在CATIA中的快速建模和网格自动剖分,最终在有限元软件ANSYS中完成有限元计算.以蟠龙抽水蓄能电站工程月牙肋钢岔管为例进行了计算,并与设计院的计算结果进行了对比与分析,结果表明该系统具有设计速度快、精度较高等优点,具有较高的实用价值.     

Stability analysis in a second-order differential equation with delays

A second-order differential equation with finite discrete delays is considered. Local stability of the zero equilibrium is investigated, and we obtain some sufficient conditions for the zero equilibrium is stable or unstable. Moreover, it is found that there exist the local Hopf bifurcations of the system when the delay varies.     

具时滞及分段常数变量苍蝇模型的Flip分支

研究了一类具有时滞及分段常数变量苍蝇模型的Flip分支.利用差分方程的特征值理论和Jury判据,给出了该模型局部稳定的充要条件.依据分支理论,讨论了Flip分支的存在性条件.基于规范化理论及中心流形定理,研究了分支的方向及其稳定性.通过举例与数值模拟验证了所得条件与结论的正确性与可实现性.     

一类具有时滞和HollingⅡ类功能反应的捕食者-食饵模型

为研究一类具有时滞和HollingⅡ类功能反应捕食者-食饵模型,由于该模型的捕食者和食饵都具有密度制约,引入时滞对模型加以讨论,通过分析特征方程和构造适当的Lyapunov泛函,得到正平衡点存在及全局稳定的充分条件。研究结果表明,时滞对系统的稳定性起了重要作用,并为生物资源管理提供了策略。     

约瑟夫森结的线性延时反馈控制分析

考虑电阻-电容分路的约瑟夫森结的线性延时反馈控制,运用非线性动力学理论分析了受控系统平凡解的稳定性。研究表明随着参数的变化,系统的稳定平凡解将会通过Hopf分岔失稳产生周期解,数值仿真验证了理论结果。     

Stability switches and Bogdanov-Takens bifurcation in an inertial two-neuron coupling system with multiple delays

In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights.The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation.We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves.To obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)bifurcation.The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form.Finally,numerical simulations are provided to support the theoretical analyses.