Variety of regimes of star-like networks of Henon maps

TL;DR

This paper explores the diverse dynamical behaviors of star-like networks of Henon maps, revealing chaos, quasiperiodicity, and synchronization phenomena, with high multistability and unpredictability in regime transitions.

Contribution

It provides a comprehensive categorization of dynamical regimes in star-like Henon networks, highlighting the extensive diversity and multistability of their behaviors.

Findings

Networks exhibit chaos, quasiperiodicity, and periodicity.

Nodes can be fully or phase synchronized.

High multistability leads to unpredictable regime changes.

Abstract

In this paper we categorize dynamical regimes demonstrated by star-like networks with chaotic nodes. This analysis is done in view of further studying of chaotic scale-free networks, since a star-like structure is the main motif of them. We analyze star-like networks of Henon maps. They are found to demonstrate a huge diversity of regimes. Varying the coupling strength we reveal chaos, quasiperiodicity, and periodicity. The nodes can be both fully- and phase-synchronized. The hub node can be either synchronized with the subordinate nodes or oscillate separately from fully synchronized subordinates. There is a range of wild multistability where the zoo of regimes is the most various. One can hardly predict here even a qualitative nature of the expected solution, since each perturbation of the coupling strength or initial conditions results in a new character of dynamics.