共查询到19条相似文献,搜索用时 93 毫秒
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本文证明了当|β|<时,有阻尼Sine-Gordon方程的Dirichlet问题的全局吸引子为一个平衡点,而且该平衡点具有指数吸引性,同时将所得结果应用到系统能稳性的研究中.最后给出了若干一般性的结果. 相似文献
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Hodgkin-Huxley系统的渐进稳定性 总被引:1,自引:1,他引:0
李全国 《纯粹数学与应用数学》2008,24(2)
用无穷维动力系统的方法研究了Hodgkin-Huxley神经脉冲传导系统的长时间行为.在齐次边界条件与非齐次边界条件证明了系统在其不变流形上的全局吸引子为系统在该不变流形内的唯一平衡点,从而证明了该系统的渐进稳定性. 相似文献
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李全国 《数学的实践与认识》2009,39(3)
用无穷维动力系统的方法研究了Belousov Zhabotinsky化学反应系统的长时间行为.在齐次边界条件与非齐次边界条件下证明了系统在其不变流形上的全局吸引子为系统在该不变流形内的唯一平衡点,从而得到了该系统的渐近稳定性. 相似文献
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本文考虑带Dirichlet边界条件的耦合Sine-Gordon方程组的渐近行为.证明了整体吸引子的存在性,并给出了整体吸引子的Hausdoof维数的上界估计.本文的估计与文[9]的结果相比有本质上的改进.在参数满足一定条件下,证明了整体吸引子恰好是系统的唯一平衡点 相似文献
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本文在齐次Neumann边界条件下考虑食饵具有避难所的捕食者-食饵扩散模型, 其功能反应函数为Holling-III 型.
主要讨论该系统全局吸引子的存在性和系统永久持续生存性, 以及
避难所对系统非负平衡点稳定性的影响. 相似文献
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研究了一类广义双色散热耦合方程组的初边值问题在齐次边界条件下的吸引子.首先通过Faedo-Galerkin方法证明了整体解的存在唯一性;其次通过证明系统的衰减性和渐近紧性,得到了系统存在全局吸引子;最后证明了该系统的全局吸引子存在有限分形维数. 相似文献
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In this paper, we continue to study the properties of the global attractor for some p-Laplacian equations with a Lyapunov function F in a Banach space when the origin is no longer a local minimum point but a saddle point of F. By using the abstract result established in our previous work, we prove the existence of multiple equilibrium points in the global attractor for some p-Laplacian equations under some suitable assumptions in the case that the origin is an unstable equilibrium point. 相似文献
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本文证明了当阻尼与扩散系数在一定的参数范围内时,有阻尼的受迫sineGordon方程的狄氏问题对于任意非自治时间周期受迫力均具有唯一的指数吸引有界集的周期解.并且,如果受迫力是自治的,则全局吸引子恰是系统唯一的指数吸引有界集的平衡解. 相似文献
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1.IntroductionandMainResultsInthispaper,weconsiderthedampedsine-Gordonequation,withhomogeneousDirichletboundarycondition:whereu=u(x,t)ER,xEn,fiisaboundeddomaininRe(m=1,2,3)withsmoothboundaryoff,thedampingcoefficientor>0,thediffusingconstantd>0.Inthesequel,insteadofconsideringsystem(1.1),weinvestigatethefollowingsysteminHilbertspaceE=Ha(fi)xL'(fl):inwhichu(t)CHI(fl),v(t)6L'(fl)foranyt>0,A=--dA,G(u)=(--sine f),fEHa(~~),noEV.=Ha(~~),itoEH.=L'(fl).Let11'Onlayrwriteequatioll(l.2)asillwhi… 相似文献
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Sine—Gordon方程的全局吸引子的维数估计 总被引:1,自引:0,他引:1
本文得到了阻尼Sine-Gordon方程的狄氏问题的全局吸引子的Hausdorff维数以偶数上界的参数条件,特别地,当阻尼与Laplae算子的第一个特征值适当大时,全局吸引子是零维的,零维吸引子恰是系统的唯一平衡解并且指数吸引相空间的有界集。 相似文献
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Random Point Attractors Versus Random Set Attractors 总被引:2,自引:0,他引:2
The notion of an attractor for a random dynamical system withrespect to a general collection of deterministic sets is introduced.This comprises, in particular, global point attractors and globalset attractors. After deriving a necessary and sufficient conditionfor existence of the corresponding attractors it is proved thata global set attractor always contains all unstable sets ofall of its subsets. Then it is shown that in general randompoint attractors, in contrast to deterministic point attractors,do not support all invariant measures of the system. However,for white noise systems it holds that the minimal point attractorsupports all invariant Markov measures of the system. 相似文献
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Bixiang Wang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7252-7260
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable manifolds of a finite number of hyperbolic equilibrium solutions, we prove that the perturbed non-autonomous system has exactly the same number of almost periodic solutions. As a consequence, the pullback attractor of the perturbed system is given by the union of unstable manifolds of these finitely many almost periodic solutions. An application of the result to the Chafee–Infante equation is discussed. 相似文献
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A dynamic control protocol for the Kumar-Seidman flexible production system represented in general algebraic form is suggested.
The ultimate purpose of the study is to minimize the total amount of work per unit time. The suggested protocol is proved
to generate the required periodic process as a global attractor. In order to substantiate convergence, a number of statements
of classical Frobenius-Perron theory are generalized to monotone piecewise affine nonlinear operators. A new method for exciting
the required production cycles in the spirit of classical Poincaré’s method is suggested. The approach is based on a new stability
criterion for an equilibrium of a discrete stationary system. A dynamic control protocol for the Kumar-Seidman flexible production
system represented in general algebraic form is suggested and proved to generate the required periodic process as a global
attractor. In order to substantiate convergence, a number of statements of classical Frobenius-Perron theory are generalized
to monotone piecewise affine nonlinear operators. 相似文献
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Attractivity,multistability, and bifurcation in delayed Hopfieldʼs model with non-monotonic feedback
For a system of delayed neural networks of Hopfield type, we deal with the study of global attractivity, multistability, and bifurcations. In general, we do not assume monotonicity conditions in the activation functions. For some architectures of the network and for some families of activation functions, we get optimal results on global attractivity. Our approach relies on a link between a system of functional differential equations and a finite-dimensional discrete dynamical system. For it, we introduce the notion of strong attractor for a discrete dynamical system, which is more restrictive than the usual concept of attractor when the dimension of the system is higher than one. Our principal result shows that a strong attractor of a discrete map gives a globally attractive equilibrium of a corresponding system of delay differential equations. Our abstract setting is not limited to applications in systems of neural networks; we illustrate its use in an equation with distributed delay motivated by biological models. We also obtain some results for neural systems with variable coefficients. 相似文献