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11.
Understanding of the basic nature of arc root fluctuation is still one of the unsolved problems in thermal arc plasma physics.
It has direct impact on myriads of thermal plasma applications being implemented at present. Recently, chaotic nature of arc
root behavior has been reported through the analysis of voltages, acoustic and optical signals which are generated from a
hollow copper electrode arc plasma torch. In this paper we present details of computations involved in the estimation process
of various dynamic properties and show how they reflect chaotic behavior of arc root in the system. 相似文献
12.
Summary We investigate the transition from two-frequency quasiperiodicity to chaotic behavior in a model for a quasiperiodically driven
magnetoelastic ribbon. The model system is a two-frequency parametrically driven Duffing oscillator. As a driving parameter
is increased, the route to chaos takes place in four distinct stages. The first stage is a torus-doubling bifurcation. The
second stage is a transition from the doubled torus to a strange nonchaotic attractor. The third stage is a transition from
the strange nonchaotic attractor to a geometrically similar chaotic attractor. The final stage is a hard transition to a much
larger chaotic attractor. This latter transition arises as the result of acrisis, the characterization of which is one of our primary concerns. Numerical evidence is given to indicate that the crisis arises
from the collision of the chaotic attractor with the stable manifold of a saddle torus. Intermittent bursting behavior is
present after the crisis with the mean time between bursts scaling as a power law in the distance from the critical control
parameter; τ ∼ (A-Ac)-α. The critical exponent is computed numerically, yielding the value α=1.03±0.01. Theoretical justification is given for the
computed critical exponent. Finally, a Melnikov analysis is performed, yielding an expression for transverse crossings of
the stable and unstable manifolds of the crisis-initiating saddle torus. 相似文献
13.
The spontaneous drift of the spiral wave in a finite domain in the complex Ginzburg-Landau equation is investigated numerically. By using the interactions between the spiral wave and its images, we propose a phenomenological theory to explain the observations. 相似文献
14.
Piotr Szopa 《Mathematical Methods in the Applied Sciences》2007,30(3):331-346
In this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
15.
应用广义胞映射方法研究了参激和外激共同作用的Duffing-van der Pol振子的随机分岔.以 系统参数通过某一临界值时,如果系统的随机吸引子或随机鞍的形态发生突然变化,则认为 系统发生随机分岔为定义,分析了参激强度和外激强度的变化对于随机分岔的影响.揭示了 随机分岔的发生主要是由于系统的随机吸引子与系统的随机鞍碰撞产生的.分析表明,广义 胞映射方法是分析随机分岔的有力工具,这种全局分析方法可以清晰地给出随机分岔的发生 和发展.
关键词:
随机分岔
全局分析
广义胞映射方法
随机吸引子
随机鞍 相似文献
16.
This paper is devoted to the long time behavior for the Drift-diffusion semi-conductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants and generation-recombination term is the Auger model; as well as the semigroup S(t) defined by the solutions map is differential. Moreover the upper bound of Hausdorff dimension for the attractor is given. 相似文献
17.
The theory of nonequilibrium potentials or quasipotentials is a physically motivated approach to small random perturbations of dynamical systems, leading to exponential estimates of invariant probabilities and mean first exit times. In the present article we develop the mathematical foundation of this theory for discrete-time systems, following and extending the work of Freidlin and Wentzell, and Kifer. We discuss strategies for calculating and estimating quasipotentials and show their application to one-dimensionalS-unimodal maps. The method proves to be especially suited for describing the noise scaling behavior of invariant probabilities, e.g., for the map occurring as the limit of the Feigenbaum period-doubling sequence. We show that the method allows statements about the scaling behavior in the case of localized noise, too, which does not originally lie within the scope of the quasipotential formalism. 相似文献
18.
Desheng Yang 《Journal of Mathematical Analysis and Applications》2007,330(1):550-570
Dynamics for the stochastic Kuramoto-Sivashinsky equation with a nonlocal term is studied. We prove that the stochastic equation has a finite-dimensional random attractor. 相似文献
19.
文章讨论无界区域上GBBM方程的Cauchy问题,对方程的解进行了先验估计,并证明了在H1弱拓扑中整体吸引子的存在性. 相似文献
20.
Louis Block James Keesling Shihai Li Kevin Peterson 《Journal of statistical physics》1989,55(5-6):929-939
A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed. 相似文献