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The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order. 相似文献
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A 3D continuous autonomous chaotic system is reported, which contains a cubic term and six system parameters. Basic dynamic properties of the new Van der Pol Jerk system are studied by means of theoretical analysis and numerical simulation. Based on the Silnikov theorem, the chaotic characterisitics of the dynamic system are discussed. Using Cardano formula and series solution of differential equation, eigenvalue problem and the existence of homoclinic orbit are studied. Furthermore, a rigorous proof for th... 相似文献
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文章对比当前高校多校区图书馆纸质图书流通模式的现状,提出读者决策的馆藏动态调整模式,分析该模式的可行性、优缺点以及对图书馆纸质图书借阅服务的影响. 相似文献
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Simplest normal forms of generalized Neimark-Sacker bifurcation 总被引：1，自引：0，他引：1
The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system.
It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates,
then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show
that the conventional Neimark-Sacker bifurcation can be further simplified. The simplest normal forms of generalized Neimark-Sacker
bifurcation are calculated. Based on the conventional normal form, using appropriate nonlinear transformations, it is found
that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the
simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of
the simplest normal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given. 相似文献
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The Kirchhoff thin elastic rod models are always the important basis to explore the configuration mechanism of the flexible structures in both the macroscopic and microscopic scale. As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the helical equilibrium configuration of DNA in salt solution. In this paper, the Kirchhoff’s equations in the presence of interfacial traction and the free energy density functions of different configurations are studied. The transition formula of the free energy between B-DNA and ZDNA is obtained, and the results show that the free energy of the transition is mainly determined by the salt concentration, which agrees well with the experimental data. 相似文献
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