An Analytical Study in Coupled Map Lattices of Synchronized States and Travelling Waves, and of their Period-Doubling Cascades

Details An Analytical Study in Coupled Map Lattices of Synchronized States and Travelling Waves, and of their Period-Doubling Cascades An Analytical Study in Coupled Map Lattices of Synchronized States and Travelling Waves, and of their Period-Doubling Cascades

2008-02-12

arxiv.org/abs/0802.1700v2

Nonlinear Sciences

Pattern Formation and Solitons

35 pages and 6 figures

Scientific paper

Several theorems are demonstrated that determine the sufficient conditions for the existence of synchronized states (periodical and chaotic) and also of travelling waves in a CML. Also are analytically proven the existence of period-doubling cascades for the mentioned patterns. The temporal state of any oscillators are completely characterized. The given results are valid for a number of arbitrary oscillators whose individual dynamics is ruled by an arbitrary C^{2} function.

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