Emergent Behaviors in Coupled Multi-scroll Oscillators in Network with Subnetworks

Adrıana Ruiz-silva; Bahia Betzavet Cassal-quiroga; Eber J. ávila-martínez; Gilardi Velázquez, Héctor Eduardo

doi:10.51537/chaos.1376501

Emergent Behaviors in Coupled Multi-scroll Oscillators in Network with Subnetworks

Journal

Chaos Theory and Applications

ISSN

2687-4539

Date Issued

2024

Author(s)

Adrıana Ruiz-silva

Bahia Betzavet Cassal-quiroga

Eber J. ávila-martínez

Gilardi Velázquez, Héctor Eduardo

Facultad de Ingeniería - CampAGS

Type

text::journal::journal article

DOI

10.51537/chaos.1376501

URL

https://scripta.up.edu.mx/handle/20.500.12552/11128

Abstract

This paper presents the emergence of two collective behaviors in interconnected networks. Specifically, the nodes in these networks belong to a particular class of piece-wise linear systems. The global topology of the network is designed in the form of connected subnetworks, which do not necessarily share the same structure and coupling strength. In particular, it is considered that there are two levels of connection, the internal level is related to the connection between the nodes of each subnetwork; while the external level is related to connections between subnetworks. In this configuration, the internal level is considered to provide lower bounds on the coupling strength to ensure internal synchronization of subnetworks. The external level has a relevant value in the type of collective behavior that can be achieved, for which, we determine conditions in the coupling scheme, to achieve partial or complete cluster synchronization, preserving the internal synchronization of each cluster. The analysis of the emergence of stable collective behavior is presented by using Lyapunov functions of the different coupling. The theoretical results are validated by numerical simulations.