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31.
The relation between the aperiodic solution of the Lorenz model and that of a stochastic anharmonic oscillator is explored. The stochastic oscillator is constructed by replacing (t) in the Lorenz model by a stochastic variable(t) of specified statistics. The resulting system is of course not isomorphic to the Lorenz model, but does share with it a number of statistical properties. Thus, within the confines of these measures the two systems are physically very similar. 相似文献
32.
The nature of a very high-dimensional chaotic attractor in an infinite-dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the another the Fourier basis composed of the Fourier modes. We introduce the exterior subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor. 相似文献
33.
It is proposed that in molecular mechanics calculation points belonging to various stable or meta-sta-ble conformtrs are mixed up and form fractal structures in conformation space.The calculation results show the following two phenomena:(i)Two levels of structure with fractal feature were observed.Around the conformer without mirror symmetry points belonging to the conformer and its enantiomer are mixed up and form the first level of fractal structure; on the boundary of the attractive basin o{ each atlractor,points belonging to different attractors form the second level of fractal structure.(ii) The variation of molecular mechanics parameters will influence the structure and area of each attractive basin significantly The above phenomena may become the basis of a new method for solving the troublesome multi-minimum-point problem in molecular mechanics calculation. 相似文献
34.
本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L2(?, L2σ(R)). 相似文献
35.
有阻尼Sine-Gordon方程的全局吸引子的维数 总被引:2,自引:0,他引:2
本文通过引入新范数,得到有阻尼Sine-Gordon方程的Dirichlet问题的全局吸引子的维数的一个估计.结果表明:当“阻尼”与“扩散”同时增大或正弦项系数减小时,吸引子的维数减小.特别地,得到了零维吸引子存在的参数条件. 相似文献
36.
The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected. 相似文献
37.
Yoshisuke Ueda 《Journal of statistical physics》1979,20(2):181-196
This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon. 相似文献
38.
39.
Jörg Steinbach 《Numerical Functional Analysis & Optimization》2013,34(3-4):395-411
The mathematical model of the injection molding process is characterized by evolutionary inequalities with an elliptic principal part and a Volterra term. Existence and uniqueness of the solution of these problems are derived by means of an argument based on the Banach fixed point theorem. Regularity results are obtained by using the penalty and Rothe method. The results can be considered as a starting point for the numerical treatment and for the application to injection molding. 相似文献
40.
《Optimization》2012,61(3):199-203
The concept of monotone semicontinuity is introduced. It is shown that every monotonically semicontinuous function with values in a space equipped with arbitrary preference relation achieves its extremes on compacts 相似文献