一类捕食食饵微分经济系统的稳定性与Hopf分支

本文主要研究了一个带有对捕食者进行捕获的微分代数经济系统的稳定性和Hopf分支问题.利用了动力系统和微分代数系统中的稳定性理论和分支理论的方法,得到了稳定性和Hopf分支稳定性的相关结论.本文对Ratio-Dependent捕食食饵模型进行了一定程度的完善,并且选取经济效益μ为分支参数进行研究,最后利用Matlab进行数值模拟,这样使得到的结论更符合现实意义.     

一类带无选择性捕获和时滞的捕食食饵系统的Hopf分支分析

本文主要研究了一个改进的带时滞和无选择捕获函数的捕食-食饵生态经济系统的稳定性和Hopf分支.利用微分代数系统的稳定性理论和分支理论,得到了系统正平衡点稳定性的条件,以及当时滞τ作为分支参数时系统产生Hopf分支的条件.对Leslie-Gower捕食-食饵模型进行了一定程度的完善,使得建立的模型更符合实际情况,因此得到的结论也更加科学.     

HOPF BIFURCATION ANALYSIS OF A PREDATOR-PREY MODEL WITH TIME-DELAY

In this paper,a predator-prey model of three species is investigated.By introducing a delay as a bifurcation parameter,it is found that Hopf bifurcation occurs when τ crosses some critical values.     

Chemostat系统中Hopf分支的存在性

本文应用Hopf分支理论研究了具有内在代谢形式的Chemostat系统存在Hopf分支的条件,同时得到周期解的存在性及稳定性的结果.     

单时滞类Lorenz系统的Hopf分岔分析

本文研究单时滞类Lorenz系统的稳定性问题.利用规范型理论,分析该系统在其零平衡点处的稳定性和发生Hopf分岔的条件,并通过数值仿真验证所得结论的正确性.本文的结论可以看做是对文献[5]研究成果的推广.     

多时滞三种群系统的Hopf分支

讨论了具有两个时滞的3种群模型,分析了系统正平衡点的稳定性和Hopf分支的存在性;然后利用中心流形定理和规范型方法,给出了确定分支周期解的分支方向与稳定性的计算公式,利用数值模拟验证了所得结论.     

向日葵方程的Hopf分支

本文以ａ为参数，讨论了向日葵方程ａ＋（ａ／４）ａ＋（ｂ／ｒ）ｓｉｎａ（ｔ－ｒ）＝０的Ｈｏｐｆ分支，给出了存在Ｈｏｐｆ分支的条件，分支方向，分支周期解的表达式及其稳定性等性质。     

一类带有比例相关捕获函数的时滞微分代数经济系统的Hopf分支分析

本文研究了一类用更为合理的无选择性捕获函数来代替普通的单位捕捞鱼获量函数的微分代数经济系统. 利用范式定理和中心流形定理, 获得了生物经济系统内平衡点局部稳定和Hopf分支的稳定性,改进和推广了已有的结果. 最后, 用数值模拟来证明分析结果的有效性.     

NUMERICAL HOPF BIFURCATION OF DELAY-DIFFERENTIAL EQUATIONS

In this paper we consider the numerical solution of some delay differential equations undergoing a Hopf bifurcation. We prove that if the delay differential equations have a Hopf bifurcation point atλ=λ*, then the numerical solution of the equation also has a Hopf bifurcation point atλh =λ* O(h).     

一类多分子反应模型的Hopf分歧解

本文用Ｌｉａｐｕｎｏｖ函数和Ｈｏｐｆ分歧定理讨论一类多分子反应模型ｄｘ／ｄｔ＝δ－ａｘ－ｘ＾ｐｙ＾ｑ，ｄｙ／ｄｔ＝ｘ＾ｐｙ＾ｑ－ｂｙ对ａ＝０，ｐ＝２，ｑ≥２，得到Ｈｏｐｆ分歧解的存在性，唯一性，稳定性及分歧解的渐近表达式。     

Double Hopf bifurcation for van der Pol-Duffing oscillator with parametric delay feedback control

The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obtained as two parameters vary. Some weak resonant and non-resonant double Hopf bifurcation phenomena are observed due to the vanishing of the real parts of two pairs of characteristic roots on the margins of the “death island” regions simultaneously. By applying the center manifold theory, the normal forms near the double Hopf bifurcation points, as well as classifications of local dynamics are analyzed. Furthermore, some quasi-periodic and chaotic motions are verified in both theoretical and numerical ways.     

多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支

本文首先用Cooke等人建立的关于超越函数的零点分布定理,研究了一类多时滞捕食-食饵系统正平衡点的稳定性及局部Hopf分支,在此基础上再结合吴建宏等人用等变拓扑度理论建立起的一般泛函微分方程的全局Hopf分支定理,进一步研究了该系统的全局Hopf分支.     

EXISTENCE OF HOPF BIFURCATION PROBLEMS WITH JUMPING NONLINEARITIES

ＥＸＩＳＴＥＮＣＥＯＦＨＯＰＦＢＩＦＵＲＣＡＴＩＯＮＰＲＯＢＬＥＭＳＷＩＴＨＪＵＭＰＩＮＧＮＯＮＬＩＮＥＡＲＩＴＩＥＳＨｅＸｉａｎｇｊｉａｎ＆ＪｉａｎｇＺｈｕｈａｎ（ＳｔａｔｉｓｔｉｃｓａｎｄＣｏｍｐｕｔｉｎｇＳｃｉｅｎｃｅ，Ｕｎｉｖｅｒｓｉｔｙｏｆ...     

一类具有时滞的比率依赖捕食者-食饵模型的全局Hopf分支

本文研究了一类比率依赖的捕食者-食饵模型的Hopf分支问题,运用吴建宏等人利用等变拓扑度理论建立起的一般泛函微分方程的全局分支理论,得到了由系统的正平衡点分支出来的周期解的全局存在性,最后利用数值模拟验证了理论分析的正确性.     

THE HOPF BIFURCATION OF QUADRATIC SYSTEM (I)_(n=0)

δlm is the parameter space of quadratic system (I)n=0. A partition of parameters corresponding to the existence and nonexistence of the limit cycle of the system is given in detail. The Hopf bifurcation surfaces of (I)m=0 are obtained, and the sketch of Hopf bifurcation surfaces of (I)n=0 are drawn.     

一类带有捕食者阶段结构的滞后型捕食食饵模型的Hopf分支

本文研究了一类带有阶段结构和Ho1lingⅢ型滞后函数响应的捕食食饵模型的稳定性和Hopf分支的问题.利用微分动力系统的标准型和中心流形定理,获得了内平衡点局部稳定和周期解的方向性,推广了文献[4]所得出的结论.     

THE LIMIT CYCLES AND HOPF BIFURCATION OF A CLASS OF SIMPLIFIED HOLLING TYPE-IV PREDATOR-PREY SYSTEM WITH LINEAR STATE FEEDBACK

In this paper, a class of simplified Type-IV predator-prey system with linear state feedback is investigated. We prove the boundedness of the positive solutions to this system, and analyze the quality of the equilibria and the existence of limit cycles of the system surrounding the positive equilibra. By Hopf bifurcation theory, the result of having two limit cycles to the system is obtained.     

具有扩散病毒感染群体动力学模型的稳定性与Hopf分歧

讨论了一个具有诺依曼边界条件扩散病毒感染群体动力学模型.证明了模型正常数平衡点的稳定性和扩散引起的Hopf分歧的存在性.     

HOPF BIFURCATION IN A PREDATOR-PREY MODEL WITH TWO DELAYS

In this paper,a predator-prey ecosystem with two delays is considered.Firstly,the stability of the equilibrium of the system is investigated by analyzing the characteristic equation.Secondly,by choosing the sum of the two delays as a bifurcation parameter,it is shown that Hopf bifurcation occurs as the parameter passes through a certain critical value.Finally,in order to illustrate our theoretical analysis,some numerical simulations are also included.     

竞争扩散时滞模型的稳定性和Hopf分歧

本文研究一类含扩散的竞争时滞模型的定常解的稳定性以及Ｈｏｐｆ分坡解的存在性,进而给出分歧周期解的稳定性和分歧方向。