Intermingled basins in coupled Lorenz systems

TL;DR

This paper studies coupled Lorenz oscillators and discovers intermingled basins of attraction, revealing complex synchronization phenomena with riddled basins and scaling laws.

Contribution

It demonstrates the existence of intermingled basins in coupled Lorenz systems and provides quantitative analysis through scaling laws.

Findings

Existence of global synchronization and antisynchronization attractors.

Basins of attraction are riddled with holes belonging to the other basin.

Scaling laws characterize the riddling of basins.

Abstract

We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and antisynchronization attractors with intermingled basins of attraction, such that the basin of one attractor is riddled with holes belonging to the basin of the other attractor and vice versa. We investigated this phenomenon by verifying the fulfillment of the mathematical requirements for intermingled basins, and also obtained scaling laws that characterize quantitatively the riddling of both basins for this system.