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.     

征地移民管理中的分歧博弈及其决策模型

征地移民的协商管理中的分歧问题中主要是征地方与被征地方之间分歧．分歧主要体现在双方认知和利益诉求的差异．分析了征地移民双方的分歧特点,研究了征地移民的分歧管理模式.利用完善的博弈理论,探讨征地移民分歧管理的基本概念、方法和决策规律.借鉴线性支出系统的效用函数,研究分歧管理博弈矩阵的建立、博弈类型、博弈分析方法,为征地移民协商管理的科学体系提供科学分析方法.     

带Ivlev反应项的捕食模型的全局分歧

在Dirichlet边界条件下研究一类带Ivlev反应项的捕食模型.利用谱分析和分歧理论的方法,证明了发自半平凡解的局部分歧正解的存在性,同时运用线性特征值扰动理论给出局部分歧解的稳定性.最后将局部分歧延拓为全局分歧,从而得到正解存在的充分条件.     

具有饱和与竞争项的捕食系统的全局分歧及稳定性

利用比较原理,分歧理论,特征值线性扰动理论,主要研究了一类具有饱和与竞争反应项的捕食-食饵系统在Dirichlet边界条件下的平衡态分歧解.首先给出了一个先验估计和局部分歧解存在的充分条件.然后对局部分歧解进行了全局延拓,得到了该系统平衡态的全局分歧解及其走向.最后讨论了局部分歧解的稳定性.     

一类带非单调转化率的捕食-食饵模型的全局分歧

主要研究了一类带非单调转化率的捕食-食饵模型,分别以生长率a和b为分歧参数,运用度理论和分歧理论讨论了这类模型在齐次第一边界条件下全局分歧结构．     

Cahn-Hilliard方程的动态分歧

利用线性全连续场的谱理论,中心流形约化方法与非线性耗散系统吸引子分歧理论,研究了Cahn-Hilliard方程的动态分歧,给出了发生分歧的条件及临界点,并给出了在Neumann边界条件下,方程分歧出的稳定奇点吸引子和鞍点的表达式.     

n维动力系统C~r扰动下周期轨的分歧定理

离散动力系统周期轨的分歧问题是近年来动力系统的重要方向之一.但大量结果只限于具体的含参系统和低维情形,限于对周期轨的2倍分歧的观察和描述.而关于较复杂的高维系统周期轨分歧的研究,结果甚少.本文继[1],研究 n 维流形上所有含参系统的分歧周期轨(即临界周期轨),得到了较完整的结果.亦即对可微系统在 C~r 扰动下周期轨的分歧进行分类,给出了发生各类分歧的必要条件及几类分歧的充要条件.还给出了分歧倍数个数的最佳上界.     

FitzHugh-Nagumo方程的分歧北大核心

运用非线性分歧理论,研究FitzHugh-Nagumo方程的定态分歧和Hopf分歧.证明了FitzHugh-Nagumo方程在适当条件下有定态分歧发生,此时FitzHugh-Nagumo方程的定态方程有非平凡解存在.另外还证明了FitzHugh-Nagumo方程在适当的条件下有Hopf分歧发生,此时该方程从平凡解分歧出非平凡的周期解.最后分析得出影响FitzHugh-Nagumo方程分歧发生的主要因素是离子电压门控通道打开与关闭的延迟反应的快慢.理论分析所得结果与实验现象是相一致的.     

扰动逻辑型方程在对称区域上的多解性问题

应用Banach空间中非完全分歧理论研究扰动逻辑型方程在对称区域上的多解性问题, 得到了精确分歧图.     

一类具有保护区域的Leslie-Gower捕食-食饵模型的分歧分析

研究了一类Neumann边界条件下带有保护区域的Leslie-Gower捕食-食饵模型,分析稳态系统从半平凡解处发生分歧的条件,得到了分歧方向及分歧值的唯一性,得到了在确定参数范围内,从半平凡解出发的分支解曲线的稳定性.     

Dynamics of a Discrete Two-species Competitive Model with Michaelies-Menten Type Harvesting in the First Species

In this paper, we use a semidiscretization method to derive a discrete two-species competitive model with Michaelis-Menten type harvesting in the first species. First, the existence and local stability of fixed points of the system are investigated by employing a key lemma. Subsequently, the transcritical bifurcation, period-doubling bifurcation and pitchfork bifurcation of the model are investigated by using the Center Manifold Theorem and bifurcation theory. Finally, numerical simulations are presented to illustrate corresponding theoretical results.     

Global Bifurcation for a Class of Lotka-Volterra Competitive Systems

For a class of Lotka-Volterra competitive systems including both diffusion and advection, a global bifurcation result of positive steady states is established via a bifurcation approach. Also, the phenomenon of multiple positive steady states is discussed.     

Dynamics of a competitive Lotka-Volterra system with three delays

In this paper, a competitive Lotka-Volterra system with three delays is investigated. By choosing the sum τ of three delays as a bifurcation parameter, we show that in the above system, Hopf bifurcation at the positive equilibrium can occur as τ crosses some critical values. And we obtain the formulae determining direction of Hopf bifurcation and stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included.     

一类带有竞争和自反时滞的网站竞争系统的Hopf分支

不同于以往研究网站竞争系统时,仅考虑带有自反时滞或竞争时滞的情况,本文研究了一类同时带有竞争时滞和自反时滞的网站竞争系统,并以时滞作为分支参数,通过分析正平衡点处的特征方程,研究了正平衡点的稳定性,证明了Hopf分支的存在性,得到了发生Hopf分支时的临界的时滞值,最后通过数值模拟进一步验证了所得结论.     

Spatially nonhomogeneous equilibrium in a reaction-diffusion system with distributed delay

We consider a reaction-diffusion system with general time-delayed growth rate and kernel functions. The existence and stability of the positive spatially nonhomogeneous steady-state solution are obtained. Moreover, taking minimal time delay τ as the bifurcation parameter, Hopf bifurcation near the steady-state solution is proved to occur at a critical value τ=τ₀. Especially, the Hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold. The general results are applied to competitive and cooperative systems with weak or strong kernel function respectively.     

Hopf bifurcation in doubly fed induction generator under vector control

This paper first presents the Hopf bifurcation phenomena of a vector-controlled doubly fed induction generator (DFIG) which is a competitive choice in wind power industry. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variable rotor speed and provide independent control of active and reactive power output. Main results are illustrated by “exact” cycle-by-cycle simulations. The detailed mathematical model of the closed-loop system is derived and used to analyze the observed bifurcation phenomena. The loci of the Jacobian’s eigenvalues are computed and the analysis shows that the system loses stability via a Hopf bifurcation. Moreover, the boundaries of Hopf bifurcation are also given to facilitate the selection of practical parameters for guaranteeing stable operation.     

Stability Analysis of an Enterprise Competitive Model with Time Delay

A three-dimensional enterprise competitive model with time delay is considered. Where the delay is regarded as bifurcation parameters. By analyzing the corresponding characteristic equation of positive equilibrium,the local stability of positive equilibrium is regarded. By using the normal form method and center manifold theorem, we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are shown to illustrate the obtained results.     

STABLE PERIODIC BEHAVIOR IN A PIONEER-CLIMAX MODEL

Two dimensional pioneer-climax models of differential and difference equations are presented and analyzed. An effort is made to separate a species response to density from the competitive effects. Stable periodic behavior is established for both models via Hopf bifurcation. For the differential equation model, a general formula is presented for determining the stability of the bifurcating period orbit.     

Complexity analysis of dynamic noncooperative game models for closed-loop supply chain with product recovery

In this paper, we consider a closed-loop supply chain (CLSC) with product recovery, which is composed of one manufacturer and one retailer. The retailer is in charge of recollecting and the manufacturer is responsible for product recovery. The system can be regarded as a coupling dynamics of the forward and reverse supply chain. Under different decision criteria, two noncooperative game models: Stackelberg game model and peer-to-peer game model are developed. The dynamic phenomena, such as the bifurcation, chaos and sensitivity to initial values are analyzed through bifurcation diagrams and the largest Lyapunov exponent (LLE). The influences of decision parameters on the complex nonlinear dynamics behaviors of the two models are further analyzed by comparing parameter basin plots, and the results show that with the improvement of retailer’s competitive position, the CLSC system will be more easier to enter into chaos.     

Asymptotic behaviour and bifurcation in competitive Lotka-Volterra Systems

A conjecture about global attraction in autonomous competitive Lotka-Volterra systems is clarified by investigating a special system with a circular matrix. Under suitable assumptions, this system meets the condition of the conjecture but Hopf bifurcation occurs in a particular instance. This shows that the conjecture is not true in general and the condition of the conjecture is too weak to guarantee global attraction of an equilibrium. Sufficient conditions for global attraction are also obtained for this system.