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

TL;DR

This paper analytically investigates coupled map lattices, establishing conditions for synchronized states and traveling waves, and proving the existence of period-doubling cascades, applicable to various oscillator systems.

Contribution

It provides new analytical theorems for the existence of synchronized states, traveling waves, and period-doubling cascades in coupled map lattices with arbitrary oscillator dynamics.

Findings

Conditions for synchronized states are derived.

Existence of traveling waves is proven.

Period-doubling cascades are analytically demonstrated.

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 C^{2} function.