Driven maps and the emergence of ordered collective behavior in globally coupled maps

1998 ◽  
Vol 58 (2) ◽  
pp. 1665-1671 ◽  
Author(s):  
A. Parravano ◽  
M. G. Cosenza
Keyword(s):  
Collective Behavior ◽  
Coupled Maps

Collective behavior in ensembles of globally coupled maps

1994 ◽  
Vol 76 (4) ◽  
pp. 411-419 ◽  
Author(s):  
Arkady S. Pikovsky ◽  
Jürgen Kurths
Keyword(s):  
Collective Behavior ◽  
Coupled Maps

scholarly journals Chimeras and Clusters Emerging from Robust-Chaos Dynamics

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
M. G. Cosenza ◽  
O. Alvarez-Llamoza ◽  
A. V. Cano
Keyword(s):  
Collective Behavior ◽  
Coupled System ◽  
Coupled Systems ◽  
Response Dynamics ◽  
Local Dynamics ◽  
Chimera States ◽  
Coupled Maps

We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks of globally coupled robust-chaos oscillators. We describe the collective behavior of a model of globally coupled robust-chaos maps in terms of statistical quantities and characterize clusters, chimera states, synchronization, and incoherence on the space of parameters of the system. We employ the analogy between the local dynamics of a system of globally coupled maps with the response dynamics of a single driven map. We interpret the occurrence of clusters and chimeras in a globally coupled system of robust-chaos maps in terms of windows of periodicity and multistability induced by a drive on the local robust-chaos map. Our results show that robust-chaos dynamics does not limit the formation of cluster and chimera states in networks of coupled systems, as it had been previously conjectured.

scholarly journals Dynamic Properties of Coupled Maps

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Chunrui Zhang ◽  
Huifeng Zheng
Keyword(s):  
Computer Simulations ◽  
Collective Behavior ◽  
Periodic Boundary ◽  
Nearest Neighbor ◽  
Dynamic Properties ◽  
Coupled System ◽  
Periodic Boundary Conditions ◽  
Theoretical Predictions ◽  
Coupling Parameters ◽  
Coupled Maps

Dynamic properties are investigated in the coupled system of three maps with symmetric nearest neighbor coupling and periodic boundary conditions. The dynamics of the system is controlled by certain coupling parameters. We show that, for some values of the parameters, the system exhibits nontrivial collective behavior, such as multiple bifurcations, and chaos. We give computer simulations to support the theoretical predictions.

Voronoi Analysis of a Soccer Game

2004 ◽  
Vol 9 (3) ◽  
pp. 233-240 ◽  
Author(s):  
S. Kim
Keyword(s):  
Collective Behavior ◽  
Quantitative Assessment ◽  
The Other ◽  
Analysis Method ◽  
Random System ◽  
Soccer Game ◽  
Voronoi Polygons ◽  
The Mean

This paper describes a Voronoi analysis method to analyze a soccer game. It is important for us to know the quantitative assessment of contribution done by a player or a team in the game as an individual or collective behavior. The mean numbers of vertices are reported to be 5–6, which is a little less than those of a perfect random system. Voronoi polygons areas can be used in evaluating the dominance of a team over the other. By introducing an excess Voronoi area, we can draw some fruitful results to appraise a player or a team rather quantitatively.

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