共查询到20条相似文献,搜索用时 15 毫秒
1.
利用Hopf与同宿两种分支中出现的系数研究了近哈密顿系统Hopf和同宿分支产生的极限环的个数与分布,得到了全局分支产生极限环的一个新的充分条件. 相似文献
2.
This paper intends to explore the bifurcation of limit cycles for planar polynomial systems with even number of degrees. To obtain the maximum number of limit cycles, a sixth-order polynomial perturbation is added to a quintic Hamiltonian system, and both local and global bifurcations are considered. By employing the detection function method for global bifurcations of limit cycles and the normal form theory for local degenerate Hopf bifurcations, 31 and 35 limit cycles and their configurations are obtained for different sets of controlled parameters. It is shown that: H(6) 35 = 62 − 1, where H(6) is the Hilbert number for sixth-degree polynomial systems. 相似文献
3.
Discrete models are proposed to delve into the rich dynamics of nonlinear delayed systems under Euler discretization, such as backwards bifurcations, stable limit cycles, multiple limit-cycle bifurcations and chaotic behavior. The effect of breaking the special symmetry of the system is to create a wide complex operating conditions which would not otherwise be seen. These include multiple steady states, complex periodic oscillations, chaos by period doubling bifurcations. Effective computation of multiple bifurcations, stable limit cycles, symmetrical breaking bifurcations and chaotic behavior in nonlinear delayed equations is developed. 相似文献
4.
In this work, we use an indirect method to investigate bifurcations of limit cycles at infinity for a class of quintic polynomial system, in which the problem for bifurcations of limit cycles from infinity be transferred into that from the origin. By the computation of singular point values, the conditions of the origin (correspondingly, infinity) to be the highest degree fine focus are derived. Consequently, we construct a quintic system with a small parameter and eight normal parameters, which can bifurcates 1 to 8 limit cycles from infinity respectively, when let normal parameters be suitable values. The positions of these limit cycles without constructing Poincaré cycle fields can be pointed out exactly. 相似文献
5.
该文研究一类五次多项式微分系统在高次奇点与无穷远点的极限环分支问题. 该系统的原点是高次奇点, 赤道环上没有实奇点. 首先推导出计算高次奇点与无穷远点奇点量的代数递推公式,并用之计算系统原点、无穷远点的奇点量,然后分别讨论了系统原点、无穷远点中心判据. 给出了多项式系统在高次奇点分支出5个极限环同时在无穷远点分支出2个极限环的实例. 这是首次在同步扰动的条件下讨论高次奇点与无穷远点分支出极限环的问题. 相似文献
6.
7.
This paper concerns with limit cycles through Hopf and homoclinic bifurcations for near-Hamiltonian systems. By using the coefficients appeared in Melnikov functions at the centers and homoclinic loops, some sufficient conditions are obtained to find limit cycles. 相似文献
8.
《Chaos, solitons, and fractals》2006,27(3):758-767
This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed. 相似文献
9.
Han Maoan 《数学年刊B辑(英文版)》1998,19(2):189-196
§1.NormalFormsofDisplacementFunctionsConsideraplanarC∞systemoftheformx=f(x)+λf0(x,δ,λ)≡f(x,δ,λ),(1.1)wherex∈R2,λ∈R,δ∈Rm,andtr... 相似文献
10.
Henk W. Broer 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):628-634
In this paper we complete the global qualitative analysis of a quartic ecological model. In particular, studying global bifurcations of singular points and limit cycles, we prove that the corresponding dynamical system has at most two limit cycles. 相似文献
11.
Valery A. Gaiko 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7532-7542
In this paper, we complete the global qualitative analysis of the well-known FitzHugh–Nagumo neuronal model. In particular, studying global limit cycle bifurcations and applying the Wintner–Perko termination principle for multiple limit cycles, we prove that the corresponding dynamical system has at most two limit cycles. 相似文献
12.
We study bifurcations of limit cycles arising after perturbations of linear piecewise Hamiltonian systems. In this paper we find bounds for the numbers of limit cycles for several families of which phase portraits were classified in Xiong and Han (2013) [14]. 相似文献
13.
《Chaos, solitons, and fractals》2006,27(5):1317-1335
This paper intends to explore the bifurcation of limit cycles for planar polynomial systems with even number of degrees. To obtain the maximum number of limit cycles, a sixth-order polynomial perturbation is added to a quintic Hamiltonian system, and both local and global bifurcations are considered. By employing the detection function method for global bifurcations of limit cycles and the normal form theory for local degenerate Hopf bifurcations, 31 and 35 limit cycles and their configurations are obtained for different sets of controlled parameters. It is shown that: H(6) ⩾ 35 = 62 − 1, where H(6) is the Hilbert number for sixth-degree polynomial systems. 相似文献
14.
The phase portraits, existence and uniqueness of stable limit cycles and Hopf bifurcations of the well-known Holling–Tanner models for predator–prey interactions are studied. The ranges of the parameters involved are provided under which the unique interior equilibrium can be determined to be a stable (or an unstable) node or focus. The Hopf bifurcations and the existence and uniqueness of stable limit cycles of the models are obtained by computing the Lyapunov number involved. Our results confirm some previous results observed and suggested from the real ecological systems. 相似文献
15.
《Chaos, solitons, and fractals》2007,31(4):960-976
Research on the bifurcations of the multiple limit cycles for a parametrically and externally excited mechanical system is presented in this paper. The original mechanical system is first transformed to the averaged equation in the Cartesian form, which is in the form of a Z2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, using the bifurcation theory of planar dynamical system and the method of detection function, the bifurcations of the multiple limit cycles of the system are investigated and the configurations of compound eyes are also obtained. 相似文献
16.
Weconsiderthequadraticsystemoftype(I)m=0acordingtotheclasificationof[1].Withoutlosofgenerality,wemayasumethatthesystemistaken... 相似文献
17.
Bo Sang 《Journal of Nonlinear Modeling and Analysis》2021,3(2):179-191
Based on the focus quantities and other techniques, the stability properties of equilibria and the limit
cycles arising from Hopf bifurcations are investigated for two models of permanent magnet synchronous motors. The first model is of
surface-magnet type and can have at most two unstable small limit cycles,
which are symmetric with respect to $x$-axis. The other model
is of interior-magnet type and can have at most four small limit
cycles in two symmetric nests. 相似文献
18.
本文用分析方法系统地研究了一类扰动三次向量场各种可能的极限环与奇异环分布,得到了较完整的结果,这对研究弱化的Hilbert第十六问题以及进一步认识三次向量场的分枝性质都是有意义的。 相似文献
19.
韩茂安 《高校应用数学学报(A辑)》1999,14(4):421-426
在具余维2奇点的四维系统的两参数开折的研究中出现一类三点异宿环的扰动分支,对此异宿环产生极限环的唯一性一直未得到完整的解决,本文圆满地解决了这一问题,并获得了全局分支中极限环的唯一性。 相似文献
20.
This paper considers the limit cycle bifurcation problem of planar piecewise differential systems with three zones. Some computation formulas studied the problem of limit cycle bifurcations are provided by introducing multiple parameters. As an application to the obtained method, the number of limit cycles of a piecewise linear system with three zones studied in Lima et al. (2017) is discussed and some more limit cycles are found. 相似文献