Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

周期激励下的前包钦格呼吸神经元的簇振荡现象研究

研究周期激励作用下的非自治前包钦格呼吸神经元模型,结果表明当外界激励频率与系统固有频率存在着量级差距时,系统可以产生典型的簇放电模式.由于激励频率远小于系统的固有频率,因此将整个周期激励项视为慢变参数,从而可以利用稳定性分析理论研究慢变参数变化下的平衡点的分岔类型,进一步应用快慢动力学分析方法给出簇模式产生的动力学机理.本文的结果说明外界激励对神经元的动力学行为有着重要影响,为进一步揭示呼吸节律的产生机制提供了重要帮助.     

Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.     

具有时滞的比率型三种群捕食模型的分支分析

本文研究了一类具有时滞的比率型三种群捕食模型.通过分析该模型的特征方程,证明了该模型在正平衡点的稳定性.通过选择时滞τ为分支参数,得到了当时滞τ通过一系列的临界值时,Hopf分支产生.应用中心流形和规范型理论,得到了关于确定Hopf分支特性的计算公式.最后进行数值模拟验证了我们所得结果的正确性.所得结果是对前人工作的补充.     

旋转流动的低模分析及仿真研究

为了探讨Couette-Taylor流从层流到湍流过渡的方式以及流动发展到湍流之后混沌吸引子的某些特征等问题,采用低模分析方法研究了Couette-Taylor流的部分动力学行为及仿真问题,讨论了Couette-Taylor流三模态类Lorenz型方程组的动力学行为,包括定态的失稳、极限环的出现、分岔与混沌的演变和全局稳定性分析等。通过线性稳定性分析和数值模拟等方法给出了此三维模型分岔与混沌等动力学行为及其演化历程,并借此解释了Couette-Taylor流试验中观察到的部分涡流的演化过程.基于系统的分岔图、Lyapunov指数谱、功率谱、Poincaré(庞加莱)截面和返回映射等揭示了系统混沌行为的普适特征.     

一类分数阶神经网络模型的稳定性与Hopf分支分析

分析了一类分数阶神经网络的稳定性与Hopf分支问题.基于分数阶稳定性判据,得到了分数阶神经网络模型局部渐近稳定的条件.并以q为分支参数,得到了分数阶系统产生Hopf的条件.最后数值仿真证明了我们的结论.     

LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM

In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations.     

An eco‐epidemiological predator–prey model where predators distinguish between susceptible and infected prey

A predator–prey model with disease amongst the prey and ratio‐dependent functional response for both infected and susceptible prey is proposed and its features analysed. This work is based on previous mathematical models to analyse the important ecosystem of the Salton Sea in Southern California and New Mexico where birds (particularly pelicans) prey on fish (particularly tilapia). The dynamics of the system around each of the ecologically meaningful equilibria are presented. Natural disease control is considered before studying the impact of the disease in the absence of predators and the interaction of predators and healthy prey and the disease effects on predators in the absence of healthy prey. Our theoretical results are confirmed by numerical simulation. Copyright © 2016 John Wiley & Sons, Ltd.     

The periodic solution bifurcated from homoclinic orbit for coupled ordinary differential equations

We consider the problem of the periodic solutions bifurcated from a homoclinic orbit for a pair of coupled ordinary differential equations in . Assume that the autonomous system has a degenerate homoclinic solution γ in . A functional analytic approach is used to consider the existence of periodic solution for the autonomous system with periodic perturbations. By exponential dichotomies and the method of Lyapunov–Schmidt, the bifurcation function defined between two finite dimensional subspaces is obtained, where the zeros correspond to the existence of periodic solutions for the coupled ordinary differential equations near . Copyright © 2016 John Wiley & Sons, Ltd.