Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model

In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized by a small change in one of the variables, determines the features of the mixed-mode oscillations. Period-doubling and saddle-node bifurcations lead to closed families (called isolas) of periodic solutions in a bifurcation corresponding to a singular Hopf bifurcation.     

Models and Proposals for Malaria: A Review

Mathematical models to study the dynamics of malaria continue to be developed and upgraded on the parasite component, which is the causative agent for malaria; on the human component that serves as a reservoir of infection for the blood feeding female mosquitoes; on the disease transmitting vector, the component mostly responsible for the movement of the parasite agent from one human to another; or on the life cycle of the malaria parasite as a pathogen both within the human and vector populations. The consideration of so-far neglected features can be beneficial for the control of malaria.     

二阶不稳型非线性时滞微分方程的振动性

研究了二阶不稳型非线性时滞微分方程的振动性,获得了方程有界解振动的一个新的充分条件。     

一类超前型微分方程的振动准则(英文)

讨论了一阶泛函微分方程x′(t) =p(t)× (τ(t) ) ,t≥ 0 ,τ(t) >t的振动性 ,建立了几个新的振动准则 ,改进了以前 [3]中的相应结果 .     

An age‐structured model of population dynamics with dominant ages,delayed behavior,and oscillations

An age‐structured model of population dynamics with age‐dominance is proposed and analyzed. Existence and uniqueness of solutions are established as well as the uniqueness and local asymptotic stability of steady‐states. Conditions for convergence to or oscillation about the steady‐state are specified in some cases.     

Un cas élémentaire d'oscillations

The probability laws describing the numbers of oscillations of the continuous symmetric random walk express themselves through the numbers of Stirling of first kind. The asymptotic behavior can easily be derived using characteristic functions.     

应用一种新的摄动方法求解数学摆的近似解析解

应用同伦技术和摄动技术,提出了一种求解数学摆的近似解析解的新摄动方法。这种方法有别于传统的摄动理论,它不依赖于小参数,而是应用同伦技术,构造一个含嵌入参数ｐ∈「０,１」的方程,然后把嵌入参数作为“小参数”。因此这种新的方法可以充分应用各种摄动方法,结果显示这种方法简单而有效,并且其一阶近似往往具有很高的精度。