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Properties of Borderlines and Phase Locking in Discontinuous Systems

Author: FangZhengJi
Tutor: WangXuMing
School: Ningxia University
Course: Condensed Matter Physics
Keywords: Discontinuous Boundary like a collection of Random network Attractor chaotic class Restricted area Multiple magic ladder Scaling law
CLC: O415
Type: Master's thesis
Year: 2005
Downloads: 50
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Abstract

Unexpected behavior after the slow changes commonly found in natural and artificial systems usually piecewise smooth mathematical model to describe. Long-term research in this area is highly nonlinear the attention of the scientific community. In recent years, not continuous conservative system became the focus of attention. This thesis piecewise smooth system of conservative and dissipative system characteristics, mechanisms, and get some more in-depth understanding. By periodically driven particle is not continuous but reversible Paul's two-dimensional area map model found in the random network structure, our research shows that the continuous random network system does not border like in 1999 in a one-dimensional infinite potential well collection, and show two typical fine structure: one is that some local network, not continuous boundary cross-section of the same cycle chain adjacent hyperbolic fixed point manifold so that the random network of chaotic diffusion strongly inhibition; second is present in the network of some local stochastic layers of the mesh, and wherein the elliptical island, the resistance of such a partial structure having infinite self-similarity. Discontinuous and irreversible Paul area of ??two-dimensional mapping discontinuous boundary like a collection in the long time limit has become called the Chaos class attracted the literature [28] reported analytical results pointed out that a class of discontinuous dissipation The first order of like boundary chaotic motion will be limited, the paper contribution to a discontinuous conservative systems of evidence for this conclusion. Our numerical study found that is not a continuous boundary of order 1 like the one side as the track access to the restricted area, because the inverse of the phase zone at any point of the two do not exist, the inward track is not possible to enter the phase region, this is the boundary, like collection essence of constrained chaotic motion. As part of the restricted area become only one inverse of the so-called escape the district, which is actually only the restricted area of ??the track escape channel; partially into two so-called inverse dissipation District. The single inverse District, the presence of border like chaotic motion constraints because certain order. We also observed that the chaotic class attractors attractors coexist with the rules of the class, they are subject to the same restrictions boundary like a collection. When the standard image of strong dissipation limit, a round-dimensional mapping discontinuities, the system may show the border collision bifurcation corresponding by multiple magic ladder (including many similar tower-type structure) describing the behavior of the phase-locked . We studied the structural characteristics of a continuous circle the Mappings observed multiple magic ladder tower type, and investigated to determine the lock-in the step rail and the system does not four consecutive points collision mode, they respectively generate four categories stepped: overhead bottom rose branches, falling branches, all kinds of steps are all different plus periodic sequence. Each sequence of steps constitute a smooth curve as a whole. These are not continuous linear mappings observed multiple magic ladder concordant structure the same characteristics. But a function of various smooth curves than W αoc-1/ln (ε) of the latter complex, can be fitted to a polynomial function. This difference may be caused by non-linear piecewise smooth mapping function. The article also reveals the mechanism of the formation of a the magic ladder similar tower structure the loop continuation of the collision model is that parameter changes. Numerical orbital period of each of the sequence of the step width with corresponding points increases and shorten the scaling law, the results show that all sequences of the universal power law △ K (n) is α n is ^{- τ ( τ gt; 0). This piecewise smooth linear mappings in the scaling law LN | △ ε (n) | α n is completely different. This difference may be caused by the nonlinearity of the mapping function.}

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