Nonlinear Dynamics of Two-Dimensional Chaotic Maps and Fractal Sets for Snow Crystals

2017 ◽  
pp. 83-91
Author(s):  
Nguyen H. Tuan Anh ◽  
Dang Van Liet ◽  
Shunji Kawamoto
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Maps ◽  
Two Dimensional ◽  
Fractal Sets ◽  
Snow Crystals

Nonlinear dynamics of a two dimensional airfoil with freeplay in an inviscid compressible flow

2000 ◽  
Vol 4 (2) ◽  
pp. 125-133 ◽  
Author(s):  
Zoran Dimitrijević ◽  
Guy Daniel Mortchéléwicz ◽  
Fabrice Poirion
Keyword(s):  
Nonlinear Dynamics ◽  
Compressible Flow ◽  
Two Dimensional ◽  
Inviscid Compressible Flow

scholarly journals Projection of compact fractal sets: application to diffusion-limited and cluster-cluster aggregates

2008 ◽  
Vol 15 (4) ◽  
pp. 695-699 ◽  
Author(s):  
F. Maggi
Keyword(s):  
Fractal Dimension ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Cohesive Sediment ◽  
Mathematical Approach ◽  
Two Dimensional ◽  
Atmospheric Sciences ◽  
Practical Applications ◽  
Fractal Sets ◽  
Diffusion Limited

Abstract. The need to assess the three-dimensional fractal dimension of fractal aggregates from the fractal dimension of two-dimensional projections is very frequent in geophysics, soil, and atmospheric sciences. However, a generally valid approach to relate the two- and three-dimensional fractal dimensions is missing, thus questioning the accuracy of the method used until now in practical applications. A mathematical approach developed for application to suspended aggregates made of cohesive sediment is investigated and applied here more generally to Diffusion-Limited Aggregates (DLA) and Cluster-Cluster Aggregates (CCA), showing higher accuracy in determining the three-dimensional fractal dimension compared to the method currently used.

FAILURE OF A MEAN-FIELD APPROACH FOR THE MILLER–HUSE PHASE TRANSITION

2000 ◽  
Vol 10 (01) ◽  
pp. 251-256 ◽  
Author(s):  
FRANCISCO SASTRE ◽  
GABRIEL PÉREZ
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Chaotic Maps ◽  
Initial Conditions ◽  
Mean Field ◽  
Region Of Interest ◽  
Universality Class ◽  
Two Dimensional ◽  
Field Approach

The diffusively coupled lattice of odd-symmetric chaotic maps introduced by Miller and Huse undergoes a continuous ordering phase transition, belonging to a universality class close but not identical to that of the two-dimensional Ising model. Here we consider a natural mean-field approach for this model, and find that it does not have a well-defined phase transition. We show how this is due to the coexistence of two attractors in its mean-field description, for the region of interest in the coupling. The behavior of the model in this limit then becomes dependent on initial conditions, as can be seen in direct simulations.

THE DYNAMICS AND STATISTICS OF BIVARIATE CHAOTIC MAPS IN COMMUNICATIONS MODELING

2004 ◽  
Vol 14 (04) ◽  
pp. 1177-1194 ◽  
Author(s):  
RACHEL M. HILLIAM ◽  
ANTHONY J. LAWRANCE
Keyword(s):  
Chaotic Maps ◽  
Two Dimensional ◽  
Arnold Cat Map ◽  
Chebyshev Map ◽  
Shift Keying ◽  
Dynamical Properties ◽  
Chaos Shift Keying

Statistical and dynamical properties of bivariate (two-dimensional) maps are less understood than their univariate counterparts. This paper gives a synthesis of extended results with exemplifications by bivariate logistic maps, the bivariate Arnold cat map and a bivariate Chebyshev map. The use of synchronization from bivariate maps in communication modeling is exemplified by an embryonic chaos shift keying system.

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