Spatiotemporal description of long-delayed systems: Ruling the dynamics

Year: 2018

Authors: Marino F., Giacomelli G.

Autors Affiliation: CNR–Istituto Nazionale di Ottica, l.go E. Fermi 6, I-50125 Firenze, Italy; CNR–Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy.

Abstract: The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatiotemporal representation, uncovering the role of multiple timescales as independent degrees of freedom. However, their identification as equivalent space and time variables does not lead to a correct dynamical rule. We introduce a framework for a proper description of the dynamics in the thermodynamic limit, providing a general avenue for the treatment of long-delayed systems in terms of partial differential equations. Such scheme is generic and does not rely on either the vicinity to bifurcations or on multiple-scale approaches. We discuss the validity of this method and consider the exemplary cases of long-delayed excitable, bistable, and Landau systems.


Volume: 98 (6)      Pages from: 060201-1  to: 060201-5

KeyWords: Delayed Systems; Pattern formation;
DOI: 10.1103/PhysRevE.98.060201

Citations: 6
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