Low dimensional behavior in three-dimensional coupled map lattices

Abstract

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows $1/f$ noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension.

7 pages, 6 figures (revised)

References in corpus (4)

• Effect of Trends on Detrended Fluctuation Analysis
• Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics
• Local dimension and finite time prediction in spatiotemporal chaotic systems
• Desynchronized wave patterns in synchronized chaotic regions of coupled map lattices