Extension of Lorenz Unpredictability

TL;DR

This paper demonstrates how unidirectional coupling in Lorenz systems can extend chaos from a drive system to a response system with simple attractors, with implications for weather unpredictability.

Contribution

It provides a theoretical proof of chaos extension in coupled Lorenz systems and explores phenomena like cyclic chaos and intermittency.

Findings

Chaos can be extended from drive to response Lorenz systems.

Extension of sensitivity and period-doubling cascade is theoretically established.

Cyclic chaos and intermittency are observed in interconnected systems.

Abstract

It is found that Lorenz systems can be unidirectionally coupled such that the chaos expands from the drive system. This is true if the response system is not chaotic, but admits a global attractor, an equilibrium or a cycle. The extension of sensitivity and period-doubling cascade are theoretically proved, and the appearance of cyclic chaos as well as intermittency in interconnected Lorenz systems are demonstrated. A possible connection of our results with the global weather unpredictability is provided.