This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize co...This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.展开更多
Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical...Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.展开更多
研究了在不可压缩流中具有立方非线性俯仰刚度的二元机翼的颤振问题。首先,对系统平衡点进行了特征值分析,得到在Hopf分岔点附近的颤振参数方程。然后,应用规范形直接法的M ap le推导程序,计算得到Hopf分岔的规范形,并数值模拟验证了超...研究了在不可压缩流中具有立方非线性俯仰刚度的二元机翼的颤振问题。首先,对系统平衡点进行了特征值分析,得到在Hopf分岔点附近的颤振参数方程。然后,应用规范形直接法的M ap le推导程序,计算得到Hopf分岔的规范形,并数值模拟验证了超、亚临界类型分岔情形下响应对初值的依赖性。最后,分析了线性和非线性刚度系数对颤振响应拓扑结构的影响。展开更多
为了深入研究窄带噪声作用下随机动力系统的特性,将复规范形法用于窄带随机动力系统.研究了Duffing、Rayleigh和Van der pol方程在谐和与窄带随机参数激励联合作用下的主共振响应和稳定性.由复规范形法得到了此系统响应振幅和相位所满...为了深入研究窄带噪声作用下随机动力系统的特性,将复规范形法用于窄带随机动力系统.研究了Duffing、Rayleigh和Van der pol方程在谐和与窄带随机参数激励联合作用下的主共振响应和稳定性.由复规范形法得到了此系统响应振幅和相位所满足的方程,再由摄动法分析了系统的主共振响应和稳定性,并用随机增维精细积分法验证了方程理论分析结果的正确性,用数值法计算了平凡解的Lyapunov指数曲面.结果表明,随着窄带随机扰动强度的增加,系统稳态解的相图从极限环变为扩散的极限环.研究证实了复规范形法用于窄带随机动力系统是有效的.展开更多
文摘This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.
文摘Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.
文摘研究了在不可压缩流中具有立方非线性俯仰刚度的二元机翼的颤振问题。首先,对系统平衡点进行了特征值分析,得到在Hopf分岔点附近的颤振参数方程。然后,应用规范形直接法的M ap le推导程序,计算得到Hopf分岔的规范形,并数值模拟验证了超、亚临界类型分岔情形下响应对初值的依赖性。最后,分析了线性和非线性刚度系数对颤振响应拓扑结构的影响。
文摘为了深入研究窄带噪声作用下随机动力系统的特性,将复规范形法用于窄带随机动力系统.研究了Duffing、Rayleigh和Van der pol方程在谐和与窄带随机参数激励联合作用下的主共振响应和稳定性.由复规范形法得到了此系统响应振幅和相位所满足的方程,再由摄动法分析了系统的主共振响应和稳定性,并用随机增维精细积分法验证了方程理论分析结果的正确性,用数值法计算了平凡解的Lyapunov指数曲面.结果表明,随着窄带随机扰动强度的增加,系统稳态解的相图从极限环变为扩散的极限环.研究证实了复规范形法用于窄带随机动力系统是有效的.
