Bifurcations in the Lozi map

TL;DR

This paper investigates bifurcations in the Lozi map, revealing how abrupt transitions between order and chaos occur via an attractor composed of many neutrally stable limit cycles sharing the same period.

Contribution

It introduces the concept of a continuum of neutrally stable limit cycles mediating bifurcations in the Lozi map, highlighting a novel transition mechanism.

Findings

Identification of attractors made of a continuum of neutrally stable limit cycles

Demonstration of abrupt order-to-order and order-to-chaos transitions

Insight into bifurcation mechanisms in piecewise linear maps

Abstract

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.