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1.
The bifurcation associated with a homoclinic orbit to saddle-focus including a pair of pure imaginary eigenvalues is investigated by using related homoclinic bifurcation theory. It is proved that, in a neighborhood of the homoclinic bifurcation value, there are countably infinite saddle-node bifurcation values, period-doubling bifurcation values and double-pulse homoclinic bifurcation values. Also, accompanied by the Hopf bifurcation, the existence of certain homoclinic connections to the periodic orbit is proved.  相似文献   

2.
一类时变动力系统的高余维分岔及其控制   总被引:2,自引:0,他引:2  
研究了一类时变动力系统的高余维分岔及其控制问题,首先利用新方法对时变分岔方程的两个方向的分岔转迁和跃迁现象进行分析,分别通过慢变解的线性化近似和量级平衡估计分岔转迁值,然后研究这类时变分岔方程的线性反蚀控制问题,通过分析相应的二维高次自治系统的Hopf分岔,在适当的条件下得到了稳定的动态滞后环,研究揭示出脉冲振动产生的机理是分岔参数随时间周期变化经过定常分岔值时所发生的分岔转迁的滞后和跃迁现象。  相似文献   

3.
Hopf-flip bifurcations of vibratory systems with impacts   总被引:2,自引:1,他引:1  
Two vibro-impact systems are considered. The period n single-impact motions and Poincaré maps of the vibro-impact systems are derived analytically. Stability and local bifurcations of single-impact periodic motions are analyzed by using the Poincaré maps. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. It is found that near the point of codim 2 bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. Period doubling bifurcation of period one single-impact motion is commonly existent near the point of codim 2 bifurcation. However, no period doubling cascade emerges due to change of the type of period two fixed points and occurrence of Hopf bifurcation associated with period two fixed points. The results from simulation shows that there exists an interest torus doubling bifurcation occurring near the value of Hopf-flip bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transit to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems.  相似文献   

4.
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   

5.
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.  相似文献   

6.
研究了二元机翼非线性颤振系统的Hopf分岔.应用中心流形定理将系统降维,并利用复数正规形方法得到了以气流速度为分岔参数的分岔方程.研究发现,分岔方程中一个系数不含分岔参数的一次幂,故使得分岔具有超临界和亚临界双重性质.用等效线性化法和增量谐波平衡法验证了所得结果.  相似文献   

7.
Bifurcations of heterodimensional cycles with highly degenerate conditions are studied by establishing a suitable local coordinate system in three-dimensional vector fields. The existence, coexistence and noncoexistence of the periodic orbit, homoclinic loop, heteroclinic loop and double periodic orbit are obtained under some generic hypotheses. The bifurcation surfaces and the existence regions are located; the number of the bifurcation surfaces exhibits variety and complexity of the bifurcation of degenerate heterodimensional cycles. The corresponding bifurcation graph is also drawn.  相似文献   

8.
约束边界与分岔参数有关的约束分岔问题,称为约束含参分岔问题.通过引入适当的变换,将约束含参分岔问题转化为新变量的非约束分岔问题,推导出了约束含参分岔问题转迁集的一般形式,结果表明只有约束分岔集受约束含参的影响,其它转迁集与不含参约束分岔的转迁集相同.以含参约束树枝分岔为例分析了此类问题的分岔分类,讨论了约束含参对分岔分类的影响.  相似文献   

9.
In this paper, a four-neuron BAM neural network with distributed delays is considered, where kernels are chosen as weak kernels. Its dynamics is studied in terms of local stability analysis and Hopf bifurcation analysis. By choosing the average delay as a bifurcation parameter and analyzing the associated characteristic equation, Hopf bifurcation occurs when the bifurcation parameter passes through some exceptive values. The stability of bifurcating periodic solutions and a formula for determining the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, numerical simulation results are given to validate the theorem obtained.  相似文献   

10.
Dynamics of an SIR epidemic model with limited medical resources revisited   总被引:1,自引:0,他引:1  
The dynamics of an SIR epidemic model is explored in this paper in order to understand how the limited medical resources and their supply efficiency affect the transmission of infectious diseases. The study reveals that, with varying amount of medical resources and their supply efficiency, the target model admits both backward bifurcation and Hopf bifurcation. Sufficient criteria are established for the existence of backward bifurcation, the existence, the stability and the direction of Hopf bifurcation. The mechanism of backward bifurcation and its implication for the control of the infectious disease are also explored. Numerical simulations are presented to support and complement the theoretical findings.  相似文献   

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