一类随机系统的有限时间镇定

讨论随机系统的有限时间镇定问题.首先提出了随机系统有限时间稳定的概念;其次证明了随机系统有限时间稳定的Lyapunov定理;然后,讨论了一类随机系统的镇定问题.     

五行系统与群的结构

利用二元关系讨论五行系统,建立了五行系统与五阶循环群之间的一一对应关系,作为推广,提出了多重关系系统的概念并讨论了其相容性、完备性和恰当性.     

可修复人机储备系统算子的本征值问题

讨论了可修复人机储备系统算子的本征值问题,讨论了系统算子非零本征值的存在性,并且系统算子一个本征值对应一个本征向量.     

非线性森林发展系统的渐近性

本讨论他一类非线性森林发展系统,利用临界增生率要概念和算子的实特征值,讨论了系统解的渐近性质。     

一类具有Beddington-Deangelis功能反应捕食系统的收获模型

研究了一类具有Beddington-Deangelis功能反应捕食系统的收获模型,讨论该系统生物经济平衡点的性态,得到了系统正平衡点全局渐进稳定的充分条件;然后利用Pontryagin最大值原理得到了最优收获策略,讨论了贴现率能影响收获种群的利润水平.     

具有多时滞的食物链系统的Hopf分支

讨论了具有时滞的食物链模型,首先我们得到了系统永久持续生存的条件,然后讨论系统在正平衡点附近发生Hopf分支的存在性;最后利用数值模拟证明所得结论.     

具终端观测且与年龄相关的非线性种群扩散系统的最优控制

讨论了一类具终端观测且与年龄相关的非线性时变种群扩散系统的最优分布控制问题利用偏微控制理论和先验估计,证明了系统最优分布控制的存在性,得到了控制为最优的一阶必要条件,并进而讨论了系统的最优反馈控制问题.     

一类依比例依赖的捕食系统的性态分析

对一类依比例依赖的时滞捕食系统进行讨论.首先,对系统中解的最终有界性、平衡点的存在性及稳定性进行了分析.进一步,利用微分比较定理讨论了系统的永久持续生存和灭绝,得到了系统的永久持续生存和灭绝的条件.     

具有参数及受迫激励的二阶系统的次谐波与混沌解

具有受迫激励的二阶非线性振子由次谐波分叉导致混沌,已有许多文献讨论过。而具有脉冲非线性参数激励的二阶系统的次谐分叉现象曾由徐皆苏等作过系统讨论。本文则讨论在实际中更有价值的两种激励同时作用的二阶系统     

一类柔性梁系统的谱分析和半群生成

讨论了一类双臂三关节柔性梁系统的分析问题．首先,建立了一个与柔性梁的偏微分方程组及初值边值条件相应的希尔伯特空间中的一阶发展系统．接着讨论系统算子的谱性质和半群性质．最后借助系统算子的谱性质和半群性质提出并证明了柔性梁系统的指数稳定性．     

A new car-following model with consideration of the prevision driving behavior

In the paper, a new car-following model is presented with the consideration of the prevision driving behavior on a single-lane road. The model’s linear stability condition is obtained by applying the linear stability theory. And through nonlinear analysis, a modified Korteweg–de Vries (mKdV) equation is derived to describe the propagating behavior of traffic density wave near the critical point. Numerical simulation shows that the new model can improve the stability of traffic flow by adjusting the driver’s prevision intensity parameter, which is consistent with the theoretical analysis.     

具时滞的人类呼吸系统模型的稳定性与分支

研究了描述人类呼吸系统的具时滞的二维微分方程的平凡解的稳定性和Hopf分支．利用规范型理论和中心流形定理给出了关于分支周期解的稳定性及Hopf分支方向等的计算公式,且进行了数值模拟计算．     

LOCAL AND GLOBAL HOPF BIFURCATIONS FOR A PREDATOR-PREY SYSTEM WITH TWO DELAYS

In this paper, the Leslie predator-prey system with two delays is studied. The stability of the positive equilibrium is discussed by analyzing the associated characteristic transcendental equation. The direction and stability of the bifurcating periodic solutions are determined by applying the center manifold theorem and normal form theory. The conditions to guarantee the global existence of periodic solutions are given.     

Stability and bifurcation analysis in an amplitude equation with delayed feedback

An amplitude equation is considered. The linear stability of the equation with direct control is investigated, and hence a bifurcation set is provided in the appropriate parameter plane. It is found that there exist stability switches when delay varies, and the Hopf bifurcation occurs when delay passes through a sequence of critical values. Furthermore, the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, some numerical simulations are performed to illustrate the obtained results.     

Stability and bifurcation in a non-kolmogorov type prey-predator system with time delay

The purpose of this paper is to study a non-Kolmogrov type prey-predator system. First, we investigate the linear stability of the model by analyzing the associated characteristic equation of the linearized system. Second, we show that the system exhibits the Hopf bifurcation. The stability and direction of the Hopf bifurcation are determined by applying the norm form theory and center manifold theorem. Finally, numerical simulations are performed to illustrate the obtained results.     

Hopf bifurcation and stability for a delayed tri-neuron network model

A neural network model with three neurons and a single time delay is considered. Its linear stability is investigated and Hopf bifurcations are demonstrated by analyzing the corresponding characteristic equation. In particular, the explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and the center manifold theorem. In order to illustrate our theoretical analysis, some numerical simulations are also included in the end.     

Hopf bifurcation in love dynamical models with nonlinear couples and time delays

A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results.     

Stochastic stability and bifurcation for the chronic state in Marchuk’s model with noise

A stochastic differential equation modelling a Marchuk’s model is investigated. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Firstly, the stochastic Marchuk’s model has been simplified by applying stochastic center manifold and stochastic average theory. Secondly, by using Lyapunov exponent and singular boundary theory, we analyze the local stochastic stability and global stochastic stability for stochastic Marchuk’s model, respectively. Thirdly, we explore the stochastic bifurcation of the stochastic Marchuk’s model according to invariant measure and stationary probability density. Some new criteria ensuring stochastic pitchfork bifurcation and P-bifurcation for stochastic Marchuk’s model are obtained, respectively.     

An extended multi-anticipative delay model of traffic flow

An extended multi-anticipative delay model is proposed by introducing multiple velocity differences and incorporating the reaction-time delay of drivers. The stability condition of the new model is obtained by applying the linear stability theory, and the modified Korteweg–de Vries (mKdV) equation is derived by the use of the nonlinear analysis method. The analytical and numerical results show that both the reaction-time delay of drivers and the information of multiple velocity differences have an important influence on the stability of the model, and that the stabilization of traffic flow is enhanced by appending the velocity difference information of multiple vehicles ahead or by decreasing the delay time.     

Backward differentiation type formulas for Volterra integral equations of the second kind

Summary Numerical integration formulas are discussed which are obtained by differentiation of the Volterra integral equation and by applying backward differentiation formulas to the resulting integro-differential equation. In particular, the stability of the method is investigated for a class of convolution kernels. The accuracy and stability behaviour of the method proposed in this paper is compared with that of (i) a block-implicit Runge-Kutta scheme, and (ii) the scheme obtained by applying directly a quadrature rule which is reducible to the backward differentiation formulas. The present method is particularly advantageous in the case of stiff Volterra integral equations.