EXISTENCE OF POSITIVE PERIODIC SOLUTION OF MUTUALISM SYSTEM WITH INFINITE DELAYS

In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solution of a mutualism system with infinite delays. Our results generalize those of Yang etc. [8] and Gopalsamy and He [7].     

一类Chemostat捕食模型正周期解的存在性

讨论了一类Chemostat捕食模型在一定条件下正周期解的存在性问题.运用周期抛物型算子理论、Schauder估计和分歧理论得到了该模型正周期解存在的充分必要条件.     

一类具有逐段常变量神经网络系统概周期解存在性与指数稳定性

利用Halanay不等式,我们得到了一类具有逐段常变量神经网络系统解全局指数稳定的一个充分条件;此外,在同样条件下,通过不动点定理,证明了这类概周期系统概周期解的存在唯一性与模包含关系．     

逐段常变量微分方程组概周期型解存在唯一性

通过差分方程指数二分法,我们研究了一类具有变系数逐段常变量微分方程组概周期与伪概周期解的存在唯一性与渐近稳定性,改进了已有文献的结果,并且得到了差分方程满足指数二分性的一个充分条件．     

The smooth solutions of a class of coupled KdV equations.

This paper is devoted to the study of the periodic initial boundary value problem and Cauchy problem for the coupled KdV equations. By the Galerkin method and sequential approximation, we get a seies of priori estimates and establish the existence of classical local solution to the periodic problem for the system. Then we obtain the existence and uniqueness of global smooth solution when the coefficients of the system satisfy certain conditions by energy menthod, conserved quantities and nonconservative quatity I(u,v).     

一类具有脉冲和非单调功能反应的捕食者-食饵系统的多重正周期解

研究了一类具有脉冲和非单调功能反应的捕食系统,利用重合度理论中的延拓定理,获得了该系统至少存在两个正周期解的充分条件.     

共振条件下一类方程无界解和周期解的共存性

讨论了在共振条件下一类具有等时位势的方程无界解和周期解的共存性．利用Poincare映射轨道的性质,给出了无界解的存在性条件．在此条件下,Poincare-Bohl定理,得到了方程的一个周期解,进而说明共振条件下这类方程无界解和周期解的是可以共存的．最后,给出了一个无界解和周期解共存的具有等时位势的方程实例．     

具有常数输入的非自治SIR流行病模型周期解的存在性

利用MAWHIN重合度理论中的延拓定理研究了一类具有常数输入的非自治SIR流行病模型的非平凡周期解的存在性.并用MatLab对其进行了数值模拟,作出了模型的相图和解曲线图形.     

Existence of two periodic solutions for a non-autonomous SIR epidemic model

A non-autonomous SIR model with periodic transmission rate and a constant removal rate is formulated. By using the continuation theorem of coincidence degree theory, sufficient conditions for the existence of at least two positive periodic solutions are obtained. The stability of the periodic solution for small seasonality is investigated. Numerical simulations are done to show our theoretical results.     

一类推广的干摩擦问题周期解的存在性

为了得到干摩擦问题存在周期解的判断方法,利用微分包含理论对系统+k~2x+μSngp(t)+T(t)a.e.进行了讨论.在周期外力p(t)周期等于固有周期2π/R的情形下得到了周期解存在的充要条件,在周期外力p(t)周期不等于固有周期整数倍2nπ/R的情形下得到了周期解存在的充分条件.     

一类具脉冲效应和单调功能反应的时滞捕食系统的正周期解

利用重合度理论中的延拓定理,获得了一类具有脉冲效应和单调功能反应的时滞捕食系统正周期解存在性的充分条件.最后,通过列举三个例子表示我们等待结果的有效性.     

中立型无穷时滞积分微分方程的周期解与稳定性

考虑了如下中立型周期微分系统ddtx(t)-∫t-∞B(t,s)x(s)ds=A(t,x(t))x(t)+∫t-∞C(t,s)x(s)ds+g(t,x(t-τ))+b(t)的周期解存在性及其稳定性问题,给出其周期解存在的充分条件.     

Dynamics of immunotherapy antitumor models with impulsive control strategy

In this paper, using the methods of killing tumors and impulsive differential equations, two immunotherapy antitumor models for describing therapies of general tumors and advanced solid tumors are established. By using the theories of impulsive equations, small amplitude perturbation techniques, and the comparison technique, we obtain the conditions which guarantee the global asymptotical stability of the tumor-eliminated periodic solution and system permanence, when immunotherapy alone is performed. The numerical results of the influences of the impulsive perturbation on the inherent oscillation show rich dynamics, such as period-doubling bifurcation and chaos. Moreover, the effects of the combination of radiotherapy with immunotherapy on antitumor are obtained, including the threshold value of stability conditions of tumor-eradication periodic solution when the mixed combination treatment of immunotherapy and radiotherapy is performed. Some numerical simulations for the effects of the timing of radiotherapy application and the timing of injection T cells on the threshold value are performed. Finally, we present some theoretical methods for suppressing the growth of tumors.     

具有时滞和脉冲的非线性食饵-竞争系统的正周期解

利用重合度理论中的延拓定理研究了脉冲作用对非线性时滞食饵-竞争系统的影响,即考察具有时滞和脉冲的非线性食饵-竞争系统的周期性,得到了该系统存在非平凡正周期解的一个充分性判别依据.     

一类具分布时滞的Hopfield网络模型的概周期解存在性与稳定性

利用Banach空间压缩不动点定理和微分不等式的分析技巧,研究一类具分布时滞的Hopfield神经网络模型的概周期解的存在性和稳定性。得到了系统存在概周期和全局指数稳定的新的充分条件。所得结果改进和推广了相关文献的结论。     

具脉冲效应的时滞周期捕食与被捕食系统正周期解的存在性

本文研究一类具脉冲效应的时滞周期捕食与被捕食系统，利用重合度理论中的方法，获得该系统至少存在一个正周期解的充分条件。     

具有强迫项Lienard类型方程周期解及概周期解的存在性

本文利用指数型二分性理论,给出具有强迫项的Ｌｉｅｎａｒｄ类型方程周期解及概周期解存在的充分条件,这些条件是由ＦｉｎｋＡ．Ｍ．,林发兴在文［１,２］对Ｌｉｅｎａｒｄ方程关于同样问题所获结果的自然扩展与推广     

一类具有时滞的比率依赖型捕食者-食饵系统周期正解的存在性

考虑一类具有时滞的比率依赖型捕食者-食饵系统,利用重合度理论中的延拓定理,得到系统存在正周期解的充分条件.     

Global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion

By employing the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion is established. Further, by constructing a Lyapunov functional and using the result of the existence of positive periodic solution, the attractivity of a positive periodic solution for above system is obtained.     

含参数泛函微分方程概周期正解的存在性

研究了一类含参数泛函微分方程概周期正解的存在性问题.结合有界性及渐近概周期性获得了系统存在概周期正解的几组充分条件,并将结果应用于几类种群动力学模型,分别获得了系统在概周期环境下存在概周期解的一组充分条件.