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 bifurcation of limit cycles 极限环分支(13)极限环分枝(3)
 极限环分支
 At the same time, the center conditions and bifurcation of limit cycles at the origin of the quintic polynomial system are also investigated. 同时还研究了一类五次系统原点的中心条件及在同步扰动下原点与无穷远点的极限环分支问题。 短句来源 Center-Focus Determination and Bifurcation of Limit Cycles of the Equator for Planar Polynomial Differential Systems 平面多项式微分系统中心焦点判定与赤道极限环分支 短句来源 In Chapter 1, the background and present conditions are introduced and summarized for the study of center-focus determination and bifurcation of limit cycles of the equator for planar polynomial differential systems. 在第一章，我们对平面多项式微分系统的中心焦点判定与赤道极限环分支问题研究的历史背景与现状进行了全面综述。 短句来源 In chapter 1, the historical background and the present progress of problems that concern with center-focus determination and bifurcation of limit cycles of planar polynomial differential systems are introduced and summarized. 在第一章中,对平面多项式微分系统中心焦点问题与极限环分支问题的历史背景和研究现状进行了全面综述,并对本文所做的工作作了简单的介绍。 短句来源 Center conditions and bifurcation of limit cycles at the infinity for a class of quintic polynomial system were studied. 研究一类五次多项式系统无穷远点的中心条件与赤道极限环分支. 短句来源 更多
 极限环分枝
 The Generalized Focal Values and Bifurcation of Limit Cycles for Quasi Quadratic Systems 拟二次系统的广义焦点量与极限环分枝 短句来源 This thesis is devoted to singular point quantities and integrability conditions of complex polynomial differential systems with resonant singular point, and center-focus determination and bifurcation of limit cycles of planar polynomial differential systems. It is composed of five chapters. 本文主要研究具共振奇点的复平面多项式微分系统的奇点量及其可积性条件以及平面多项式微分系统的中心焦点判定与极限环分枝问题,全文由五章构成。 短句来源 Studied in this paper are center conditions and bifurcation of limit cycles from the equator for a class of cubic polynomial system. 本文研究了一类三次系统无穷远点的中心条件与赤道极限环分枝问题。 短句来源
 “bifurcation of limit cycles”译为未确定词的双语例句
 The Algebraic Critical Cycles and Bifurcation of Limit Cycles for the System=a+sum from ((i+j)=2) (a_(ij)x~iy~j),=b+sum from ((i+j)=2) (b_(ij)x~iy~j) 微分方程组=a+sum from ((i+j)=2) (a_(ij)x~iy~j),=b+sum from ((i+j)=2) (b_(ij)x~iy~j)的极限环存在的分歧值与代数奇异环 短句来源 BIFURCATION OF LIMIT CYCLES FORMING COMPOUND EYES IN A PLANAR CUBIC DIFFERENTIAL SYSTEM (Ⅱ) 平面三次微分系统的极限环复眼分枝(Ⅱ) 短句来源 Bifurcation of Limit Cycles from Planar Isochrones Depending on a Small Parameter 在混合扰动下从闭轨族分支的极限环 短句来源 THE NUMBER AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF CUBIC SYSTEMS 一类三次系统的极限环个数与奇点分支 短句来源

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 bifurcation of limit cycles
 We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of differential systems coming from the Mechanics. The transition between tonic firing and burst firing is due to a saddle-node bifurcation of limit cycles. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ?n with n ? k, when we perturb it in a class of $\mathcal{C}^2$ differential systems. Bifurcation of limit cycles near equivariant compound cycles 更多
 On the basis of the experiment of laser chaos in a Q-swiched CO_2 laser whichhad been made by Arecchi et al, simulation is made on the rate equations of thephoton population n and the molecular population inverse △ under the condition thatthe cavity damping rate is modulated by an electro-optical modulator. In thecomputation process, the modulation frequency Ω is fixed at 2π×60kHz and the ampli-tude is varied slowly.Through analyzing the results, two different generalized bista-bility regions and a series of... On the basis of the experiment of laser chaos in a Q-swiched CO_2 laser whichhad been made by Arecchi et al, simulation is made on the rate equations of thephoton population n and the molecular population inverse △ under the condition thatthe cavity damping rate is modulated by an electro-optical modulator. In thecomputation process, the modulation frequency Ω is fixed at 2π×60kHz and the ampli-tude is varied slowly.Through analyzing the results, two different generalized bista-bility regions and a series of subharmonic bifurcation of limit cycles and a seriesof inverse period-doubling bifurcation of chaotic bands have been obtained.Theconvergence constant which has been computed is close to the Feigenbaum's. 据Arecchi等人在Q开关CO_2激光器中进行的激光混沌的实验,对光子数与粒子反转数的两变量速率方程组,在空腔衰减率由电光装置调制的情况下,进行了数值计算。计算中,固定调制频率Ω=2π×60kHz,控制振幅m作缓慢变化。通过数据分析,得到了两个不同的广义双稳区及一系列正的极限环与倒的混沌带的倍周期分岔序列,算得了相邻间隔的比例因子,并与Feigenbaum常数δ=4.669作了比较。 The question on bifurcation of limit cycles in quadratic conservative perturbations of a quadratic integrable system is discussed. As a result of conservative perturbations, the first order Melnikov function for a perturbed system is identically equal to zero, so the second order Melnikov function has to be considered. The perturbation parameters which make no use in the first order Melnikov function may be important in the second order Melnikov function. Hence perturbed systems are more complicated.... The question on bifurcation of limit cycles in quadratic conservative perturbations of a quadratic integrable system is discussed. As a result of conservative perturbations, the first order Melnikov function for a perturbed system is identically equal to zero, so the second order Melnikov function has to be considered. The perturbation parameters which make no use in the first order Melnikov function may be important in the second order Melnikov function. Hence perturbed systems are more complicated. With the help of the formula for the second Melnikov function and theoretical analysis, the following result is obtained: if the first order Melnikov function for a perturbed system is identically equal to zero, and the second order Melnikov function for the perturbed system is not identically equal to zero, the system has at most two limit cycles. 研究了一个具有同宿轨的二次可积系统在二次保守扰动下的分支现象 .此时一阶Melnikov函数恒等于零 ,必须考虑二阶Melnikov函数 ,而在一阶Mel nikov函数中不起作用的扰动参数在二阶Melnikov函数中却起着非常重要的作用 ,因此扰动部分极为复杂 .在此借助于二阶Melnikov函数的计算公式及理论分析 ,建立了极限环分支定理 ,得到了在一阶Melnikov函数恒等于零 ,而二阶Melnikov函数不恒等于零时 ,可能分支出的极限环个数最大为 2的结论 Start with the general theory and then specialized to the particular case of cubic polynomial systems for which the simultaneous bifurcation of limit cycles from the origin and the equator is studied. By means of method of changing the stability of singular at the origin, combining with the method of researching the bifurcation at infinity in vector fields of cubic system, the sufficient conditions for the existence of several limit cycles around the origin or near the equator respectively... Start with the general theory and then specialized to the particular case of cubic polynomial systems for which the simultaneous bifurcation of limit cycles from the origin and the equator is studied. By means of method of changing the stability of singular at the origin, combining with the method of researching the bifurcation at infinity in vector fields of cubic system, the sufficient conditions for the existence of several limit cycles around the origin or near the equator respectively to a class of cubic system which has exactly an unique singular point at infinity are obtained. 从微分方程一般理论出发 ,研究了平面三次多项式系统在原点周围和赤道附近同时产生极限环分支的情形 .通过改变位于原点的奇点的稳定性 ,结合分析三次系统向量场在无穷远处的分支 ,得到了恰有一个无穷远奇点的三次系统分别在原点周围和赤道附近同时存在多个极限环的充分条件 << 更多相关文摘
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