Phase synchronization of two-dimensional lattices of coupled chaotic maps

2000 ◽  
Vol 62 (2) ◽  
pp. 2114-2118 ◽  
Author(s):  
Bambi Hu ◽  
Zonghua Liu
Keyword(s):  
Chaotic Maps ◽  
Phase Synchronization ◽  
Two Dimensional

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.

scholarly journals Cryptography Using Multiple Two-Dimensional Chaotic Maps

2012 ◽  
Vol 4 (8) ◽  
pp. 1-7 ◽  
Author(s):  
Ibrahim S. I. Abuhaiba ◽  
Amina Y. AlSallut ◽  
Hana H. Hejazi ◽  
Heba A. AbuGhali
Keyword(s):  
Chaotic Maps ◽  
Two Dimensional

THE BIRTH AND DEATH PROCESSES OF HYPERCYCLE SPIRALS

2003 ◽  
Vol 06 (04) ◽  
pp. 515-535
Author(s):  
KAZUMASA OIDA
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Phase Synchronization ◽  
Occurrence Rate ◽  
Two Dimensional ◽  
Archimedean Spiral ◽  
Simulation Experiments ◽  
Birth And Death Processes ◽  
Long Time ◽  
Random Walk Simulation

The behavior of hypercycle spirals in a two-dimensional cellular automaton model is analyzed. Each spiral can be approximated by an Archimedean spiral with center, width, and phase change according to Brownian motion. A barrier exists between two spirals if the phase synchronization hypothesis is taken into account, and the occurrence rate of pair decay (simultaneous disappearance of two spirals) can be explained through a random walk simulation with the barrier. Simulation experiments show that adjacent species violation is necessary to create new spirals. A hypercycle system can live for a long time if spirals in the system are somewhat unstable, since new spirals cannot emerge when existing spirals are too stable.

scholarly journals Cryptanalysis of a cryptosystem based on discretized two-dimensional chaotic maps

2008 ◽  
Vol 372 (46) ◽  
pp. 6922-6924 ◽  
Author(s):  
Ercan Solak ◽  
Cahit Çokal
Keyword(s):  
Chaotic Maps ◽  
Two Dimensional
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