Periodic solutions and flip bifurcation in a linear impulsive system

In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.     

基于三角模糊数序列的灰色预测模型

以GM(1,1)模型为代表的灰色预测模型是以精确数序列为基础,难以满足实际需要.为了使灰色模型适应于模糊数序列,具体给出了一种基于三角模糊数序列的建模方法,这种方法也可以实现对二元区间模糊数和梯形模糊数序列的建模.首先由三角模糊数序列得出三个含有等量信息的精确数序列:重心序列、隶属函数的覆盖面积序列和中界点序列,对这三个序列分别建模后,再导出原始三角模糊数序列的三个界点的预测模型.这种建模方法既保持了模糊数的整体性又提高了建模序列的光滑度,提高了预测精度.最后进行了多组随机三角模糊数序列的数据模拟,验证了模型的有效性.     

具有饱和接触率和垂直传染的SIRS传染病模型分岔分析

研究了一类具有饱和发生率、脉冲生育、脉冲接种和垂直传染的SIRS传染病模型的复杂动力学行为,首先构造了一个庞卡莱映射,然后利用映射的不动点及其特征值,得到了系统无病周期解的存在和稳定的条件,接着详细讨论了系统的跨临界分岔、超临界分岔和倍周期分岔现象,最后给出了能很好验证理论分析的数值结果.     

Bifurcation control and chaos in a linear impulsive system

Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.     

具阶段结构害虫防治模型的脉冲效应

对于用微分方程描述的种群生态动力系统，其研究结果已十分丰富，但自然界中的许多变化规律都呈现出脉冲效应，因此用脉冲微分方程描述某些运动状态在固定或不固定时刻的快速变化或跳跃更切合实际，尤其在刻画种群生长和流行病动力学行为方面，脉冲微分方程的描述显得更科学更真实，具有脉冲效应的种群动力学模型的研究目前还处于刚刚起步阶段，本对符合实际的有脉冲效应的具阶段结构的常系数害早防治模型进行了研究，得到了系统存在周期解的充分条件，系统存在唯一周期解的充分条件，系统周期解轨道渐近稳定的充分条件。