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运用Leray-Schauder不动点定理研究具有无穷时滞的泛函微分方程的正周期解的存在性问题,获得了存在正周期解的充分条件,改进了文献[3]中的结果. 相似文献
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一类带时滞竞争模型的周期解 总被引:2,自引:0,他引:2
研究了来源于水生种群植化相克的模型,提出了带时滞的半线性抛物系统.用上下解方法讨论了抛物方程组周期解存在性的原理,利用特征函数构造所提出抛物系统的上解,给出了正周期解存在的充分条件. 相似文献
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利用微分方程组的基解矩阵及推广的Halanay微分不等式等分析技巧,讨论了一类具有不同时间尺度的变时滞竞争神经网络的平衡点存在和唯一性,并给出指数稳定性判定的充分条件,最后通过数值仿真实例检验结果的正确性. 相似文献
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一个时滞微分系统的稳定性与Hopf分支 总被引:6,自引:2,他引:4
给出了一个三维时滞微分系统的平衡点的全时滞稳定的代数判据。也讨论并给出了这个系统存在Hopf分支的条件,两个例子说明了本文定理的应用。 相似文献
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研究一类具高阶Laplace算子的非线性脉冲时滞双曲型偏微分方程的振动性,利用特征函数法和一阶脉冲时滞微分不等式,获得了该类方程在Robin边值条件下所有解振动的若干充分性判据,所得结果推广和包含了最新文献中的结果. 相似文献
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研究了一类具多比例时滞细胞神经网络的全局指数周期性与稳定性.通过变换y(t)=x(e~t)将具多比例时滞的细胞神经网络变换成具常时滞变系数的细胞神经网络,利用一些分析技巧与构造合适的Lyapunov泛函,得到系统的周期解存在唯一且全局指数周期的时滞依赖的充分条件,判断方法简单易验证.并给出了两个例子及其数值仿真结果以支持所得结论. 相似文献
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Differential equation problem is an important research topic in the international academia. In accordance with certain ecological phenomena, previous research was conducted based on simple observational and statistical data. But this approach does not effectively study the essence of the ecological phenomena. Recently, one dynamic approach has been proposed for the study of ecology in the international academia. According to this approach, first of all, the ecology is reduced to the differential equation model which represents the essential phenomenon, and then the dynamic law and rules of mathematics and biology will be studied. Currently, an extensive research is conducted on the differential equation problem. This paper primarily explores a type of competitive ecological model, which is a system of differential equation with infinite integral. we first study the existence of positive periodic solution to this model, and then present sufficient conditions for the global attractivity of positive periodic solutions. 相似文献
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Zijian Liu 《Journal of biological dynamics》2018,12(1):551-576
In this paper, a one-prey-n-predator impulsive reaction-diffusion periodic predator–prey system with ratio-dependent functional response is investigated. On the basis of the upper and lower solution method and comparison theory of differential equation, sufficient conditions on the ultimate boundedness and permanence of the predator–prey system are established. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Examples and numerical simulations are presented to verify the feasibility of our results. A discussion is conducted at the end. 相似文献
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利用锥上不动点理论,本文研究了一类非线性泛函微分方程正周期解的存在多样性和ω-周期解的不存在性.获得了一些新的结果.应用这些新的结果,讨论了一类带参数的血细胞生成模型,给出该模型的正周期解的存在性,此结果利用以前的方法是无法得到的. 相似文献
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Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays 总被引:4,自引:0,他引:4
This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems. 相似文献
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F Brauer 《Journal of theoretical biology》1977,69(1):143-152
A result is given on the existence of an asymptotically stable periodic solution of a class of systems of periodic ordinary differential equations. The result is applied to a lake eutrophication model with seasonal effects, and some suggestions are made for the solution of such models. 相似文献
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运用拓扑度方法给出高维非自治系统全爱化型小参数问题周期解存在性的一些简明的判别方法,即在非线性项满足强制性条件时,无需计算便能判别周期解的存在。 相似文献
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In this paper, we develop a mathematical model concerning a chemostat with impulsive state feedback control to investigate the periodicity of bioprocess. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions under which the model has a periodic solution of order one are obtained. Furthermore, we estimate the position of the periodic solution of order one and discuss the existence of periodic solution of order two. The theoretical results and numerical simulations indicate that the chemostat system with impulsive state feedback control either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentrations of microorganisms and substrate. 相似文献
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In a difference or differential equation one is usually interested in finding solutions having certain properties, either intrinsic properties (e.g. bounded, periodic, almost periodic) or extrinsic properties (e.g. stable, asymptotically stable, globally asymptotically stable). In certain instances it may happen that the dependence of these equations on the state variable is such that one may (1) alter that dependency by replacing part of the state variable by a function from a class having some of the above properties and (2) solve the 'reduced' equation for a solution having the remaining properties and lying in the same class. This then sets up a mapping Τ of the class into itself, thus reducing the original problem to one of finding a fixed point of the mapping. The procedure is applied to obtain a globally asymptotically stable periodic solution for a system of difference equations modeling the interaction of wild and genetically altered mosquitoes in an environment yielding periodic parameters. It is also shown that certain coupled periodic systems of difference equations may be completely decoupled so that the mapping Τ is established by solving a set of scalar equations. Periodic difference equations of extended Ricker type and also rational difference equations with a finite number of delays are also considered by reducing them to equations without delays but with a larger period. Conditions are given guaranteeing the existence and global asymptotic stability of periodic solutions. 相似文献
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Using successor functions and Poincaré-Bendixson theorem of impulsive differential equations, the existence of periodical solutions to a predator-prey model with two state impulses is investigated. By stability theorem of periodic solution to impulsive differential equations, the stability conditions of periodic solutions to the system are given. Some simulations are exerted to prove the results. 相似文献
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讨论了具有反馈控制的两种群概周期竞争系统,利用微分不等式和构造适当的Lyapunov函数,获得存在全局渐近稳定的概周期解的充分条件. 相似文献