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Lienard型系统的定性行为 总被引:4,自引:0,他引:4
孙继涛 《数学物理学报(A辑)》1994,14(1):90-95
该文研究了非线性系统的定性行为,得到了方程(E)的解总归一致有界的充要条件和存在周期解的充分条件,推广和改进了文[1-5]及[10]的工作. 相似文献
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研究了一类非线性生化系统的定性行为,给出了该系统极限环的不存在性、存在性、惟一性和稳定性的充分条件,补充和完善了戴林勋(1999)的结论。 相似文献
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本文研究了耦合Schrodinger-KdV方程组的Cauchy问题,此耦合方程组刻化了一维Langmuir和离子声波相互作用的非线性动力学行为.本文建立了此问题在Hk×Hk中的整体适定性理论(k∈Z+). 相似文献
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该文讨论非线性系统狓=1犪(狓)(犺(狔)-犉(狓)), 狔=-犪(狓)犵(狓) (E)解的一些定性行为,获得了系统(E)为振动,全局渐近稳定,全局中心的充要条件和周期解的存在的充分条件. 相似文献
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一类Holling功能性反应模型极限环的唯一性 总被引:10,自引:0,他引:10
考虑捕食者无密度制约,食饵具有非线性密度制约的第三类Holling功能性反应捕食者-食饵系统.对该系统给出了完整的定性分析,证明了该系统至多有一个极限环,存在极限环的充要条件是正平衡点不稳定. 相似文献
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本文就近年来关于Banach空间中非线性逼近问题的存在性和适定性问题及其与Banach空间几何性质关系的研究结果和进展作一系统的介绍和综述,其中包含了一系列作者的近期研究成果. 相似文献
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Cahn-Hilliard-Navier-Stokes系统是描述两种互不相溶且不可压缩流体演化的著名界面系统.本文主要研究一般非线性条件下具有动态边界的Cahn-Hilliard-Navier-Stokes系统解的适定性及长时间行为,证明了弱解的整体存在性和唯一性, 建立了在H X VI中全局吸引子的存在性. 相似文献
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基于年龄分布和加权总规模的种群系统的最优收获控制 总被引:10,自引:0,他引:10
研究一类带年龄结构的非线性种群系统的最优收获问题,其生死率依赖于个体年龄和加权总规模.借助不动点原理确立了系统的适定性,应用极大化序列法和紧性证明了最优解的存在性, 利用法锥和共轭系统技巧导出了最优性条件,推广了一些文献的工作. 相似文献
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We consider the one-dimensional weakly asymmetric nearest neighbour exclusion process and study, in macroscopic space-time coordinates, the fluctuations of the associated density field around the solution of the nonlinear BURGERS equation with viscosity. We show that this fluctuations converge to a generalized ORNSTEIN-UHLENBECK process, the drift term of which can be obtained by linearization of the BURGERS equation. Our approach is based on a nonlinear transformation of the exclusion process. 相似文献
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In this paper, we study the global topological linearization of a differential equation with piecewise constant argument of generalized type (DEPCAG) when the nonlinear term is unbounded. Some sufficient conditions are established for the topological conjugacy between a nonlinear system and its linear system. Our work generalizes the main result of Pinto and Robledo in [25]. 相似文献
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An approximate method based on piecewise linearization is developed for the determination of periodic orbits of nonlinear oscillators. The method is based on Taylor series expansions, provides piecewise analytical solutions in three-point intervals which are continuous everywhere and explicit three-point difference equations which are P-stable and have an infinite interval of periodicity. It is shown that the method presented here reduces to the well-known Störmer technique, is second-order accurate, and yields, upon applying Taylor series expansion and a Padé approximation, another P-stable technique whenever the Jacobian is different from zero. The method is generalized for single degree-of-freedom problems that contain the velocity, and (approximate) analytical solutions are presented. Finally, by introducing the inverse of a vector and the vector product and quotient, and using Taylor series expansions and a Padé approximation, the method has been generalized to multiple degree-of-freedom problems and results in explicit three-point finite difference equations which only involve vector multiplications. 相似文献
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Input-Output linearization is a method that uses nonlinear statefeedback control to obtain linear equations between the inputand output of a nonlinear control system. Its success dependscrucially on the ability of the control to steer across thelevel sets of the output function. This is essentially a globalcontrollability problem. In this work, we present a linearizationtheory that is geomentrical. This mean that the relation ofthe control vector fields to the output function is consideredfrom a global geometrical perspective. Our argument involvesgeneric vector fields and output functions and linearizationfor typical trajectories. We prove that the relative degreeis generically one. This approach also succeeds in resolving the problems of controlpast the singular set, and thus goes further than the existingliterature. The unavoidable cost is that linearization may bepiecewise, since the concept of strong relative degree cannot(in general) be defined globally. A simple example is includedwith a common type of output function, and linearization isworked out in some detail as an illustration of some of thenovel approach. 相似文献
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M. Villarini 《Journal of Mathematical Analysis and Applications》2011,373(2):521-534
We study families of holomorphic vector fields, holomorphically depending on parameters, in a neighborhood of an isolated singular point. When the singular point is in the Poincaré domain for every vector field of the family we prove, through a modification of classical Sternberg's linearization argument, cf. Nelson (1969) [7] too, analytic dependence on parameters of the linearizing maps and geometric bounds on the linearization domain: each vector field of the family is linearizable inside the smallest Euclidean sphere which is not transverse to the vector field, cf. Brushlinskaya (1971) [2], Ilyashenko and Yakovenko (2008) [5] for related results. We also prove, developing ideas in Martinet (1980) [6], a version of Brjuno's Theorem in the case of linearization of families of vector fields near a singular point of Siegel type, and apply it to study some 1-parameter families of vector fields in two dimensions. 相似文献
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高阶(2+1)维Broer-Kaup方程的局域相干结构 总被引:1,自引:0,他引:1
利用推广的齐次平衡方法,研究高阶(2+1)维Broer-Kaup方程的局域相干结构.首先基于推广的齐次平衡方法,给出这个模型的一个非线性变换,并把它变换成一个线性化的方程.然后从线性化方程出发,构造出一个分离变量的拟解.由于拟解中不仅含有两个y的任意函数,而且还有{αi,βi,γk,kj,lk}和{N,M,L}这些参数可以任意选取,因此合适的选择这些函数和参数,可以得到新的相当丰富的孤子结构.方法直接而简单,可推广应用一大类(2+1)维非线性物理模. 相似文献
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Xing Lü Mingshu Peng 《Communications in Nonlinear Science & Numerical Simulation》2013,18(9):2304-2312
Conservation law plays a vital role in the study of nonlinear evolution equations, particularly with regard to integrability, linearization and constants of motion. In the present paper, it is shown that infinitely many conservation laws for certain nonlinear evolution equations are systematically constructed with symbolic computation in a simple way from the Riccati form of the Lax pair. Note that the Lax pairs investigated here are associated with different linear systems, including the generalized Kaup–Newell (KN) spectral problem, the generalized Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem, the generalized AKNS–KN spectral problem and a recently proposed integrable system. Therefore, the power and efficiency of this systematic method is well understood, and we expect it may be useful for other nonlinear evolution models, even higher-order and variable-coefficient ones. 相似文献
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完全近似法的推广及其应用* 总被引:6,自引:2,他引:4
本文提出完全近似法的一种推广形式:引用渐近线性化的概念,通过对坐标作包含因变量的非线性泛函的变换,把原有的非线性问题线性化,从而以首项渐近解和相应的坐标变换给出原问题的较高阶的近似解析解.对模型方程和若干弱非线性振动和波动问题的分析表明,本文提出的方法是简捷而有效的. 相似文献
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In this paper, we introduce and study a class of generalized nonlinear vector variational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems and so on. Applying maximal element theorem, we prove the existence of its solutions in the setting of locally convex topological vector space. 相似文献