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21.
弱Silnikov现象中的全局分支问题 总被引:1,自引:0,他引:1
本文考虑在一条同宿于具一对纯虚特征值的鞍-焦点的轨道邻域内的分支问题,证明了在同宿分支值的邻域内,存在着可数无穷多个鞍结点分支值,倍周期分支值和2-脉冲同宿分支值,并且两相邻鞍结点分支值的比趋于常数1。 相似文献
22.
本文考虑奇摄动问题的位于快变量空间中的奇异同宿轨道的保存和周期轨道分支问题.文中关于奇异同宿轨道保存的结论推广了一些已知的结果,而周期轨道产生于奇异同宿轨道的分支则提供了一种新的分支类型. 相似文献
23.
A Trigger of Coupled Singularities 总被引:3,自引:0,他引:3
By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number eight in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under certain conditions, a theorem of the appearance of a trigger of coupled singularities in a nonlinear dynamical conservative system, the first derivative of the system potential energy which is a product of two periodic functions with different periods, and one bifurcation parameter, which is the cause for the appearance of new roots of these two functions, is defined. 相似文献
24.
Constructing dynamical systems having homoclinic bifurcation points of codimension two 总被引:4,自引:0,他引:4
Björn Sandstede 《Journal of Dynamics and Differential Equations》1997,9(2):269-288
A procedure is derived which allows for a systematic construction of three-dimensional ordinary differential equations having homoclinic solutions. The equations are proved to exhibit codimension-two homoclinic bifurcation points. Examples include the non-orientable resonant bifurcation, the inclination-flip, and the orbit-flip. In addition, an equation is constructed which has a homoclinic orbit converging to a saddle-focus satisfying Shilnikov's condition. The vector fields are polynomial and non-stiff in that the eigenvalues are of moderate size. 相似文献
25.
Xiaoguang Zhang Chunhua Shan Zhen Jin Huaiping Zhu 《Journal of Differential Equations》2019,266(1):803-832
There has been a substantial amount of well mixing epidemic models devoted to characterizing the observed complex phenomena (such as bistability, hysteresis, oscillations, etc.) during the transmission of many infectious diseases. A comprehensive explanation of these phenomena by epidemic models on complex networks is still lacking. In this paper we study epidemic dynamics in an adaptive network proposed by Gross et al., where the susceptibles are able to avoid contact with the infectious by rewiring their network connections. Such rewiring of the local connections changes the topology of the network, and inevitably has a profound effect on the transmission of the disease, which in turn influences the rewiring process. We rigorously prove that the adaptive epidemic model investigated in this paper exhibits degenerate Hopf bifurcation, homoclinic bifurcation and Bogdanov–Takens bifurcation. Our study shows that adaptive behaviors during an epidemic may induce complex dynamics of disease transmission, including bistability, transient and sustained oscillations, which contrast sharply to the dynamics of classical network models. Our results yield deeper insights into the interplay between topology of networks and the dynamics of disease transmission on networks. 相似文献
26.
Homoclinic Orbits of a Quadratic Isochronous
System by the Perturbation-incremental Method
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![点击此处可从《Journal of Nonlinear Modeling and Analysis》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Junhua Li Hailing Wang Zuxiong Li Zhusong Chu Zhang Chen 《Journal of Nonlinear Modeling and Analysis》2021,3(1):115-130
In this paper, the perturbation-incremental method is presented for the analysis of a quadratic isochronous system. This method combines the remarkable characteristics of the perturbation method and the incremental method. The first step is the perturbation method. Assume that the parameter $\lambda$ is small, i.e. $\lambda\approx0$, the initial expression of the homoclinic orbit is obtained. The second step is the parameter incremental method. By extending the solution corresponding to small parameters to large parameters, we can get the analytical-expressions of homoclinic orbits. 相似文献
27.
In this paper, we study the problem of homoclinic orbits to Aubry sets for time-periodic positive definite Lagrangian systems. We show that there are infinitely many homoclinic orbits to some Aubry set under the conditions that the associated Mather set is uniquely ergodic and the first relative homology group of the projection of this Aubry set is nonzero. 相似文献
28.
This paper presents exact solutions in terms of implicit functions and hyperbolic functions to a nonconvex dissipative system,
controlled by a Duffing–van der Pol nonlinear equation with a fifth-order nonlinearity. Applications to the complex Ginzburg–Landau
equation are illustrated and several classes of uniformly translating solutions are obtained accordingly.
Part of the work was announced at the International Conference on Complementarity, Duality, and Global Optimization in Science
and Engineering, Virginia Tech. University, Blacksburg, Virginia, August 15–17, 2005. This work is supported by NSF Grant
CCF–0514768. 相似文献
29.
Lienard系统的同宿轨族与闭轨族 总被引:4,自引:0,他引:4
本文讨论Lienard系统解的一些定性性质,得到了存在同宿轨族、闭轨族、双曲扇形和椭圆扇形、正负半轨有界及其与等倾线相交的充要条件或充分条件. 相似文献
30.
Homoclinic solutions for fourth order differential equations with superlinear nonlinearities
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![点击此处可从《Journal of Applied Analysis & Computation》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper we investigate the existence of homoclinic solutions for a class of fourth order differential equations with superlinear nonlinearities. Under some superlinear conditions weaker than the well-known (AR) condition, by using the variant fountain theorem, we establish one new criterion to guarantee the existence of infinitely many homoclinic solutions. 相似文献