Confined chaotic behavior in collective motion for populations of globally coupled chaotic elements

Details Confined chaotic behavior in collective motion for populations of globally coupled chaotic elements Confined chaotic behavior in collective motion for populations of globally coupled chaotic elements

1998-06-08

arxiv.org/abs/chao-dyn/9806011v1

Nonlinear Sciences

Chaotic Dynamics

18 pages, 9 figures

Scientific paper

10.1103/PhysRevE.59.1675

The Lyapunov exponent for collective motion is defined in order to characterize chaotic properties of collective motion for large populations of chaotic elements. Numerical computations for this quantity suggest that such collective motion is always chaotic, whenever it appears. Chaotic behavior of collective motion is found to be confined within a small scale, whose size is estimated using the value of the Lyapunov exponent. Finally, we conjecture why the collective motion appears low dimensional despite the actual high dimensionality of the dynamics.

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