Checkerboard Spiral Waves in a 2D Coupled Map Lattice

1997 ◽  
Vol 07 (11) ◽  
pp. 2569-2575 ◽  
Author(s):  
Valery I. Sbitnev
Keyword(s):  
Parameter Space ◽  
Control Parameter ◽  
Nearest Neighbors ◽  
Spatiotemporal Chaos ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
Spatiotemporal Intermittency

An intermittency of spatiotemporal chaos and checkerboard spiral waves is observed in a 2D coupled sigmoid map lattice. A rotating arm of such a spiral consists of sites oscillating in opposite phases with respect to nearest neighbors. A region of the spiral waves exhibited in the control parameter space is presented. The spatiotemporal intermittency stems from a crisis-induced intermittency of chaotic wanderings and zigzag burstings that is shown in this work.

Chaos Structure and Spiral Wave Self-Organization in 2D Coupled Map Lattice

1998 ◽  
Vol 08 (12) ◽  
pp. 2341-2352 ◽  
Author(s):  
Valery I. Sbitnev
Keyword(s):  
Quantitative Analysis ◽  
Entropy Production ◽  
Statistical Physics ◽  
Nonequilibrium Thermodynamics ◽  
Spiral Wave ◽  
Spatiotemporal Chaos ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
Self Organization ◽  
Entropy Variation

Methods borrowed from nonequilibrium thermodynamics and statistical physics have been employed in the quantitative analysis of spatiotemporal chaos in a 2D coupled map lattice (CML). Emphasis is made on entropy, entropy variation and entropy production. These quantities manifest peculiar changes in a region where spiral waves emerge. The spiral waves observed in the 2D CML are found to be dissipative objects with an elevated entropy production.

CHECKERBOARD SPIRAL WAVES IN A 2D COUPLED MAP LATTICE: SCALING EVIDENCE

1999 ◽  
Vol 09 (05) ◽  
pp. 919-928 ◽  
Author(s):  
VALERY I. SBITNEV ◽  
ALEX. O. DUDKIN
Keyword(s):  
Close Agreement ◽  
Diffusion Length ◽  
Spiral Wave ◽  
Spatiotemporal Chaos ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
Self Organization ◽  
Natural Unit ◽  
Saddle Node Bifurcation ◽  
Unit Of Length

Checkerboard spiral waves in a 2D CML under consideration are generic solutions in a narrow parameter layer located adjacent to the saddle-node bifurcation boundary in the spatiotemporal chaos region. The spiral wave self-organization is in close agreement with the Haken's slaving principle. Scaling correspondence between sizes of the spiral waves and the diffusion length that is a natural unit of length in the CML is established.

"SPIRAL WAVE–TRAVELING CLUSTERING" INTERMITTENCY AND 1/f-NOISE IN A 2D COUPLED MAP LATTICE

1999 ◽  
Vol 09 (05) ◽  
pp. 929-937 ◽  
Author(s):  
MARK A. PUSTOVOIT ◽  
VALERY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Exponential Decay ◽  
Power Law ◽  
Strange Attractor ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
The Self ◽  
Saddle Node Bifurcation ◽  
Self Organized

Intermittency of checkerboard spiral waves and traveling clusterings originating from sudden shrinking of the strange attractor of the 2D CML in the neighborhood of the saddle-node bifurcation boundary is found. A power-law probability density for lifetimes in the spiral wave (laminar) phase is observed, while in the checkerboard clusterings (bursting) phase the above quantity exhibits an exponential decay. This difference can be interpreted through the self-organized behavior of the spiral waves, and the passive relaxation of the disordered checkerboard clusterings.

Spatiotemporal chaos in improved cross coupled map lattice and its application in a bit-level image encryption scheme

2021 ◽  
Vol 544 ◽  
pp. 1-24
Author(s):  
Mingxu Wang ◽  
Xingyuan Wang ◽  
Tingting Zhao ◽  
Chuan Zhang ◽  
Zhiqiu Xia ◽  
...  
Keyword(s):  
Image Encryption ◽  
Spatiotemporal Chaos ◽  
Coupled Map Lattice ◽  
Encryption Scheme

Onset of spatiotemporal intermittency in a coupled-map lattice

1993 ◽  
Vol 47 (6) ◽  
pp. 4575-4578 ◽  
Author(s):  
John R. de Bruyn ◽  
Lihong Pan
Keyword(s):  
Coupled Map Lattice ◽  
Spatiotemporal Intermittency

QUENCHING LORENZIAN CHAOS

2004 ◽  
Vol 14 (08) ◽  
pp. 2875-2884 ◽  
Author(s):  
RAYMOND HIDE ◽  
PATRICK E. McSHARRY ◽  
CHRISTOPHER C. FINLAY ◽  
GUY D. PESKETT
Keyword(s):  
Parameter Space ◽  
Control Parameter ◽  
Nonlinear Dynamical Systems ◽  
General Interest ◽  
Nonlinear Ordinary Differential Equations ◽  
The Novel ◽  
Nonlinear Dynamical ◽  
F Region ◽  
Dimensionless Variables ◽  
Autonomous Set

How fluctuations can be eliminated or attenuated is a matter of general interest in the study of steadily-forced dissipative nonlinear dynamical systems. Here, we extend previous work on "nonlinear quenching" [Hide, 1997] by investigating the phenomenon in systems governed by the novel autonomous set of nonlinear ordinary differential equations (ODE's) [Formula: see text], ẏ=-xzq+bx-y and ż=xyq-cz (where (x, y, z) are time(t)-dependent dimensionless variables and [Formula: see text], etc.) in representative cases when q, the "quenching function", satisfies q=1-e+ey with 0≤e≤1. Control parameter space based on a,b and c can be divided into two "regions", an S-region where the persistent solutions that remain after initial transients have died away are steady, and an F-region where persistent solutions fluctuate indefinitely. The "Hopf boundary" between the two regions is located where b=bH(a, c; e) (say), with the much studied point (a, b, c)=(10, 28, 8/3), where the persistent "Lorenzian" chaos that arises in the case when e=0 was first found lying close to b=bH(a, c; 0). As e increases from zero the S-region expands in total "volume" at the expense of F-region, which disappears altogether when e=1 leaving persistent solutions that are steady throughout the entire parameter space.

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