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Limit cycles of quadratic systems 总被引:2,自引:1,他引:1
In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert’s Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric properties of four field rotation parameters of a new canonical system which is constructed in this paper, we present a proof of our earlier conjecture that the maximum number of limit cycles in a quadratic system is equal to four and their only possible distribution is (3:1) [V.A. Gaiko, Global Bifurcation Theory and Hilbert’s Sixteenth Problem, Kluwer, Boston, 2003]. Besides, applying the Wintner–Perko termination principle for multiple limit cycles to our canonical system, we prove in a different way that a quadratic system has at most three limit cycles around a singular point (focus) and give another proof of the same conjecture. 相似文献
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具有一个高阶奇点和两个零特征根的一类多项式系统 总被引:2,自引:0,他引:2
韩玉良 《高校应用数学学报(A辑)》1996,(3):269-276
本文讨论了具有一个高阶奇点和两个零特征根的一类2n+1次系统,证明了这类系统可以存在两个n阶细焦点,给出极限存在性和不存在性的条件,并证明了无穷远分界线环的存在性。 相似文献
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Ariel Fernández 《Theoretical chemistry accounts》1985,68(4):285-289
The topology of the pattern of intrinsic reaction coordinates and separatrices is investigated for 6-electron sigmatropic pericyclic rearrangements.It is demonstrated that the trajectories of nuclear motion involving HOMO-LUMO crossing are the separatrices of the basins of the chemical species involved. The special case of the Diels-Alder cycloaddition is analyzed. 相似文献
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Eduardo González-Olivares Jaime Mena-Lorca Alejandro Rojas-Palma José D. Flores 《Applied Mathematical Modelling》2011
This work deals with the analysis of a predator–prey model derived from the Leslie–Gower type model, where the most common mathematical form to express the Allee effect in the prey growth function is considered. 相似文献
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本文给出了中心对称三次系统存在双曲线分界线环的充要条件,并证明了此系统还可以至少存在五个极限环。 相似文献
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It is known that weak interactions of two solitary waves in generalized nonlinear Schrödinger (NLS) equations exhibit fractal dependence on initial conditions, and the dynamics of these interactions is governed by a universal two-degree-of-freedom ODE system [Y. Zhu J. Yang, Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrödinger equations, Phys. Rev. E 75 (2007) 036605]. In this paper, this ODE system is analyzed comprehensively. Using asymptotic methods along separatrix orbits, a simple second-order map is derived. This map does not have any free parameters after variable rescalings, and thus is universal for all weak interactions of solitary waves in generalized NLS equations. Comparison between this map’s predictions and direct simulations of the ODE system shows that the map can capture the fractal-scattering phenomenon of the ODE system very well both qualitatively and quantitatively. 相似文献
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