一类Z_2-等变扰动的三次哈密顿系统极限环的个数与分布(英文)

This paper is concerned with the number and distributions of limit cycles of a cubic Z2-symmetry Hamiltonian system under quintic perturbation.By using qualitative analysis of differential equation,bifurcation theory of dynamical systems and the method of detection function,we obtain that this system exists at least 14 limit cycles with the distribution C91  [C11 ＋ 2（C32 2C12）].     

一类带有竞争和自反时滞的网站竞争系统的Hopf分支

不同于以往研究网站竞争系统时,仅考虑带有自反时滞或竞争时滞的情况,本文研究了一类同时带有竞争时滞和自反时滞的网站竞争系统,并以时滞作为分支参数,通过分析正平衡点处的特征方程,研究了正平衡点的稳定性,证明了Hopf分支的存在性,得到了发生Hopf分支时的临界的时滞值,最后通过数值模拟进一步验证了所得结论.     

Dynamical study of fractional order differential equations of predator‐pest models

To explore the impact of pest‐control strategy through a fractional derivative, we consider three predator‐prey systems by simple modification of Rosenzweig‐MacArthur model. First, we consider fractional‐order Rosenzweig‐MacArthur model. Allee threshold phenomena into pest population is considered for the second case. Finally, we consider additional food to the predator and harvesting in prey population. The main objective of the present investigation is to observe which model is most suitable for the pest control. To achieve this goal, we perform the local stability analysis of the equilibrium points and observe the basic dynamical properties of all the systems. We observe fractional‐order system has the ability to stabilize Rosenzweig‐MacArthur model with low pest density from oscillatory state. In the numerical simulations, we focus on the bistable regions of the second and third model, and we also observe the effect of the fractional order α throughout the stability region of the system. For the third model, we observe a saddle‐node bifurcation due to the additional food and Allee effect to the pest densities. Also, we numerically plot two parameter bifurcation diagram with respect to the harvesting parameter and fractional order of the system. We finally conclude that fractional‐order Rosenzweig‐MacArthur model and the modified Rosenzweig‐MacArthur model with additional food for the predator and harvested pest population are more suitable models for the pest management.     

The motion characteristics of the double‐pendulum system with skew walls

Many components of machines and other technological devices (chains and bodies hanging on the ropes) can be modeled as multiple pendulums situated in tubes or holes of limited space. The investigation of motion of such systems represents the substance of many real technological problems; therefore, it stirred up motivation to perform research on vibration of a double pendulum situated between two skew rigid walls. The analyzed system was set into motion by the horizontal movement of its suspending. The results of the simulations show that the system can exhibit both the regular and chaotic movements depending on the excitation frequency. The development of the computational model, which is applicable for more complex investigations, and learning more on the motion character of a double pendulum, the movement of which is limited by skew walls, are the principal contributions of the presented article.     

二维Lengyel-Epstein模型的六边形斑图

从局部分支的观点讨论2维Lengyel-Epstein模型的非常数正平衡态问题. 首先, 当区域为矩形时用局部分支定理构造六边形平衡态斑图; 其次, 在分支点附近确定分支方向.     

Stability of laminated convex shells of revolution with microdamages in laminate components

The problem of bifurcation instability of shells of revolution made of a laminate material with progressively damaged components under loading is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 98–106, July 2006.     

ON THE COEFFICIENTS APPEARING IN THE EXPANSION OF MELNIKOV FUNCTIONS IN HOMOCLINIC BIFURCATIONS

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On the Bifurcation of Flows of a Heat-Conducting Fluid between Two Rotating Permeable Cylinders

Sufficient conditions are found for the bifurcation of flow of a viscous heat-conducting fluid between two rotating permeable cylinders.     

The discussion about horseshoes and finite subharmonic bifurcations

In this paper, finite subharmonic bifurcations have been discussed by means of some examples. It is found that for centrally symmetric system, under small disturbance, if it has two independant sequences of subharmonic bifurcations, the system passes to chaos (horeseshoe) through finite subharmonic bifurcations, and that for noncentrally symmetric system, the relation between subharmonic bifurcations and horseshoe is complicated.