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

2008/02/12 by Ma Dolores Sotelo Herrera, Herrera, M. Dolores Sotelo, Jesús San Martín +1
Computer Science · Physics and Astronomy · #Cellular Automata and Applications #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0802.1700

openalex publication_date 2008/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 C² function.

Related

• Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method
• Heterogeneous, Weakly Coupled Map Lattices
• Connecting period-doubling cascades to chaos
• Replication of Period-Doubling Route to Chaos in Coupled Systems with Delay
• Chimera states in coupled map lattices: Spatiotemporally intermittent\n behavior and an equivalent cellular automaton