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该文讨论了一类离散Leslie捕食与被捕食系统,获得了该系统的持久性,当系统为周期系统时,得到了它的周期解的存在性,并且在某些条件下,该周期解是全局稳定的. 相似文献
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本文以经典的带有时滞的捕食-被捕食系统为基础,构造了一类泛函微分方程作为描述分布在由n个岛屿构成的环状区域上的捕食-被捕食种群生长过程的模型.我们假设种群在最相邻的岛屿间相互迁移,以迁移率为分支参数,研究了该系统的锁相振动,给出了离散波分支的存在条件. 相似文献
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本文利用映射的分岔理论讨论了一类离散的捕食与被捕食系统的动力学性质,分析了其正平衡点的稳定性,并讨论了Neimark-Sacker分岔的稳定性与方向。 相似文献
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研究了一类具有时滞的疾病感染的捕食-被捕食模型.首先讨论了系统的耗散性;接着分析了系统的平衡点并根据Routh-Hurwitz准则判断其局部稳定性;最后利用Lyapunov方法和Bendixson-Dulac判别法给出了平衡点的全局稳定性. 相似文献
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具有扩散的捕食与被捕食系统的持续性和稳定性 总被引:2,自引:0,他引:2
本文研究了一类具有扩散和时滞的捕食与被捕食系统,证明了在适当条件下系统 是一致持续的,利用同伦技术证明了正平衡点的存在性,构造适当的Lyapunov函数获得 了正平衡点的局部和全局稳定的充分条件. 相似文献
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研究了一个关于害虫防治的有脉冲效应以及年龄结构和时滞的捕食-被捕食模型,得到了害虫根除的周期解全局吸引以及系统持久的充分条件,同时证明了系统所有的解是一致最终有界的.这些结果能为害虫防治的实际操作提供一定的理论依据. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(9):2235-2244
In recent years piecewise affine (PWA) modeling has developed as an attractive tool for the approximation of various complex nonlinear systems. In spite of the wide application of PWA modeling, the optimal approximation of a continuous time nonlinear system with scalar functions by the minimum number of affine systems has not been addressed properly in literature. This paper deals with a fuzzy clustering based approach for the optimal PWA approximation of a class of continuous time nonlinear systems. The technique is based on the trade-off between increasing the approximation accuracy of the various nonlinear functions and simplifying the approximation by the minimum number of subsystems. As an application, the technique is utilized to obtain a PWA approximation of the glucose regulation system. Numerical simulations depicted that, for a given number of subsystems, the derived glucose regulation model provides an optimal approximation of the original nonlinear system. The model also provided some biological insight about the interactions involved in glucose regulation. 相似文献
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Geir Dahl Jon Magne Leinaas Jan Myrheim Eirik Ovrum 《Linear algebra and its applications》2007,420(2-3):711-725
We consider a matrix approximation problem arising in the study of entanglement in quantum physics. This notion represents a certain type of correlations between subsystems in a composite quantum system. The states of a system are described by a density matrix, which is a positive semidefinite matrix with trace one. The goal is to approximate such a given density matrix by a so-called separable density matrix, and the distance between these matrices gives information about the degree of entanglement in the system. Separability here is expressed in terms of tensor products. We discuss this approximation problem for a composite system with two subsystems and show that it can be written as a convex optimization problem with special structure. We investigate related convex sets, and suggest an algorithm for this approximation problem which exploits the tensor product structure in certain subproblems. Finally some computational results and experiences are presented. 相似文献
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Hideki Murakawa 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(10):3512-3524
Reaction–diffusion system approximations to the classical two-phase Stefan problem are considered in the present study. A reaction–diffusion system approximation to the Stefan problem has been proposed by Hilhorst et al. from an ecological point of view, and they have given convergence results for the system. In the present study, a new reaction–diffusion system approximation to the Stefan problem is proposed based on regularization of the enthalpy–temperature constitutive relation. For a deeper understanding of the approximation mechanism by means of reaction–diffusion systems, the rates of convergence for both the solutions and the free boundaries are investigated. 相似文献
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Yuan-ming Wang 《计算数学(英文版)》2000,(2)
1. IntroductionDue to the development of various studies in electromagnetism, biology and someother fields, nonlinear systems hajve been paid extellsive attention both analytically andnumerically, e.g., see [1--12]. As we kll')w, a reasonable numerical method should notonly have the approximation error of higher order, but also preserve the main feature ofthe original problem. In this case? the numerical results might fit the physical processbetter. Since the usual approximations simulate the … 相似文献
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This paper considers polling systems with an autonomous server that remains at a queue for an exponential amount of time before
moving to a next queue incurring a generally distributed switch-over time. The server remains at a queue until the exponential
visit time expires, also when the queue becomes empty. If the queue is not empty when the visit time expires, service is preempted
upon server departure, and repeated when the server returns to the queue. The paper first presents a necessary and sufficient
condition for stability, and subsequently analyzes the joint queue-length distribution via an embedded Markov chain approach.
As the autonomous exponential visit times may seem to result in a system that closely resembles a system of independent queues,
we explicitly investigate the approximation of our system via a system of independent vacation queues. This approximation
is accurate for short visit times only.
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51.IntroductionInthispaPer,westudythefollowingrate-tyPeviscoelasticsystem,i.e.withtheinitialdata(v(x,o),u(x,o),p(x,O))=(vo(x),uo(x),po(x)),(1.2)wherevand(-p)denotestrainandstressrespectively,uisrelatedtotheparticlevelocity,Eisapositiveconstant,calledthedynamicYoung'smodulus,T>Oisarelaxationthae.Ttussystemwasproposedin[l4]tointroducearelaxationapprokimationtothefonowingsystemSincethesystem(1.3)canbeobtainedfrom(1.1)byanexpansionprocedtireasthefirstorder,itisnaturaltoexPectthatthesolutionof(1… 相似文献
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Yuan Lin Xuejun Gao MingQing Xiao 《Numerical Methods for Partial Differential Equations》2009,25(2):327-346
In this article a sixth‐order approximation method (in both temporal and spatial variables) for solving nonhomogeneous heat equations is proposed. We first develop a sixth‐order finite difference approximation scheme for a two‐point boundary value problem, and then heat equation is approximated by a system of ODEs defined on spatial grid points. The ODE system is discretized to a Sylvester matrix equation via boundary value method. The obtained algebraic system is solved by a modified Bartels‐Stewart method. The proposed approach is unconditionally stable. Numerical results are provided to illustrate the accuracy and efficiency of our approximation method along with comparisons with those generated by the standard second‐order Crank‐Nicolson scheme as well as Sun‐Zhang's recent fourth‐order method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
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Yoshiyuki Kagei Michael Růžička Gudrun Thäter 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(4):447-467
We discuss a model limit problem which arises as a first step in the mathematical justification of our Boussinesq-type approximation
[4], which takes into account dissipative heating in natural convection. We treat a simplified highly non linear system depending
on a (perturbation) parameter ε. The main difficulty is that for ε ≠ 0 the velocity is not solenoidal. First we prove that
our system has weak solutions for each fixed ε. Moreover, while the chosen perturbation parameter ε tends to zero we show,
that we arrive at the usual incompressible case and the standard Boussinesq approximation. 相似文献
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O.B. Gus’kov 《Journal of Applied Mathematics and Mechanics》2013,77(4):401-411
A method for the approximate solution of the problem of many bodies of spherical form in a viscous fluid is developed in the Stokes approximation. Using a purely hydrodynamic approach, based on the use of the concept of a self-consistent field, the classical boundary value problem is reduced to a formal procedure for solving a linear system of algebraic equations in the tensor coefficients, which occur in the solution obtained for the velocity field and pressure of the liquid. A procedure for the approximate solution of this system of equations is constructed for the case of dilute suspensions, when the ratio of the size of the dispersed particles to the characteristic distance between them is a small parameter. Finally, the initial boundary value problem is reduced to solving a recurrent system of equations, in which each subsequent approximation for all the required quantities depends solely on the previous approximations. The system of recurrent equations obtained can be solved analytically in any specified approximation with respect to a small parameter. It is shown that this system of equations contains in itself all possible physical formulations of the problems, and, within the frameworks of the mathematical procedure constructed, they are distinguished solely by a set of specified and required functions. The practical possibilities of the method are in no way limited by the number of dispersed particles in the fluid. 相似文献
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This paper presents a special purpose dual algorithm for obtaining a Chebychev approximation to an overdetermined system of linear equations. The method is founded on the principles of linear programming and is designed to take advantage of the problem's special structure. It is shown that, while maintaining a reduced basis, certain iterations of the standard dual algorithm may be combined into one. Two computer code implementations of the method are discussed and a computational comparison with another algorithm for Chebychev approximation is given. 相似文献