Different types of critical behavior in conservatively coupled H\'enon maps

TL;DR

This paper investigates how varying dissipation levels in coupled Hénon maps affect their transition to chaos, revealing different critical behaviors and the fragmentation of the Feigenbaum line.

Contribution

It introduces a detailed analysis of how dissipation influences the structure of bifurcation scenarios and identifies multiple types of critical points in the transition to chaos.

Findings

Feigenbaum line fragments into multiple parts with dissipation decrease

Presence of different critical point types (C and H) at Feigenbaum line ends

Mechanisms of Feigenbaum line rupture are characterized

Abstract

We study the dynamics of two conservatively coupled H\'enon maps at different levels of dissipation. It is shown that the decrease of dissipation leads to changes in the parameter plane structure and scenarios of transition to chaos comparing with the case of infinitely strong dissipation. Particularly, the Feigenbaum line becomes divided into several fragments. Some of these fragments have critical points of different types, namely of C and H type, as their terminal points. Also the mechanisms of formation of these Feigenbaum line ruptures are described.