具有饱和项的互惠系统的分歧与稳定性

运用谱分析和分歧理论的方法,在齐次Dirichlet边界条件下,对具有饱和项的互惠系统的非负定态解的分歧及其稳定性进行研究.一方面,分别以生长率作为分歧参数,讨论了发自半平凡解的分歧;另一方面,以两物种的生长率作为分歧参数,利用Liapunov-Schmidt过程,研究了在二重特征值处的分歧;同时判定了这些分歧解的稳定性.     

Dynamics of a Predator-Prey Model with Allee Effect and Herd Behavior

This paper deals with dynamics of a predator-prey model with Allee effect and herd behavior. We first study the stability of non-negative constant solutions for such system. We also establish the existence of Hopf bifurcation solutions for such predator-prey model. The stability and bifurcation direction of Hopf bifurcation solution in the case of spatial homogeneity are further discussed. At the same time, several examples are given by MATLAB. Finally, the numerical simulations of the system are carried out through MATLAB, which intuitively verifies and supplements the theoretical analysis results.     

The Existence and Global $p$-Exponential Stability of Periodic Solution for Stochastic BAM Neural Networks with Delays

In this paper, we consider a class of stochastic BAM neural networks with delays. By establishing new integral inequalities and using the properties of spectral radius of nonnegative matrix, some sufficient conditions for the existence and global $p$-exponential stability of periodic solution for stochastic BAM neural networks with delays are given. An example is provided to show the effectiveness of the theoretical results.     

Study of a Monod–Haldene type food chain chemostat with pulsed substrate

In this paper, we introduce and study a model of a Monod–Haldene type food chain chemostat with pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey, and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halfing.     

Safety margin criterion of nonlinear unbalance elastic axle system

IntroductionAtpresentanewanddevelopingsubject—chaoticdynamicsstartsabroadprospectforanalysisofnonlinearsystem[1～ 5 ].Largerotatingmachineryisatypicalnonlinearnon_autonomoussystem .Thesaferunofrotorsystemisofgreatsignificancetosociallifeandeconomicdevelopment.Thestabilityisthekeytosafeoperation .Thesafestabilityanalysisandcontrolforlargesystemisnotonlyamajorbasicresearchbutalsoisveryimportanttosolvethesafeproblemsinlifeandproduction[6 ,7].Soar,althoughmanymathematicians,mechanistsandengineer…     

完全与不完全叉形分岔实验

介绍一种可演示完全与不完全叉形分彷的实验装置，并分析其机理。本文对非线性动力学实验设计有一定启示作用。     

Quantum R-matrices and factorization problems

A relation between quantum R-matrices and certain factorization problem in Hopf algebras is established. A definition of dressinf transformation in the quantum case is also given.     

时滞Rucklidge系统Hopf分岔分析与电路实现

以一类新的单时滞Rucklidge系统为分析对象,通过计算时滞系统的平衡点,分析该系统在各平衡点的稳定性和Hopf分岔的存在性,得到其发生Hopf分岔的条件。Matlab多组数值仿真验证了理论分析的正确性。基于此设计了一种可切换时滞与非时滞的混沌电路,并运用Multisim14.0进行仿真,实验结果表明,该电路可行且有效。     

非线性时滞动力系统的研究进展

具有时滞的动力系统广泛存在于各工程领域．本文从动力学角度对时滞动力系统的研究进展作一综述,内容包括时滞动力系统的特点、研究方法、动力学热点问题的研究进展等．由于时滞动力系统的演化趋势不仅依赖于系统的当前状态,还依赖于系统过去某一时刻或若干时刻的状态,其运动方程要用泛国微分方程来描述,解空间是无穷维的．即使系统中的时滞非常小,在许多情况下也不能忽略不计．对于非线性时滞常微分方程,目前的研究思路基本上与常微分方程系统理论相平行．主要研究方法可分为时域法和频域法,前者包括Ｔａｙｌｏｒ级数法,中心流形法,Ｐｏｉｎｃａｒｅ映射法等,后者包括Ｎｙｑｕｉｓｔ法等．目前对这类系统的动力学研究主要集中在稳定性、Ｈｏｐｆ分岔、混沌等方面．研究表明：时滞动力系统具有非常丰富和复杂的动力学行为,如单变量的一维非线性时滞动力系统可发生混沌现象,与用常微分方程描述的系统有本质性差别．另一方面,人们可巧妙地利用时滞来控制动力系统的行为,如时滞反馈控制是控制混饨的主要方法之一．最后,本文展望了存在的一些问题以及近期值得关注的研究．     

Undercompressive shocks for nonstrictly hyperbolic conservation laws

We study 2×2 systems of hyperbolic conservation laws near an umbilic point. These systems have Undercompressive shock wave solutions, i.e., solutions whose viscous profiles are represented by saddle connections in an associated family of planar vector fields. Previous studies near umbilic points have assumed that the flux function is a quadratic polynomial, in which case saddle connections lie on invariant lines. We drop this assumption and study saddle connections using Golubitsky-Schaeffer equilibrium bifurcation theory and the Melnikov integral, which detects the breaking of heteroclinic orbits. The resulting information is used to construct solutions of Riemann problems.