Eur. Phys. J. Spec. Top. (2022) 231: 369-379
https://doi.org/10.1140/epjs/s11734-021-00406-4

Regular Article

On the behavior of bidirectionally coupled multistable systems

¹ Departamento de Matemáticas, Universidad de Sonora, 83000, Hermosillo, Sonora, Mexico
² Facultad de Ingeniería, Universidad Panamericana, Josemaría Escrivá de Balaguer 101, 20290, Aguascalientes, Aguascalientes, Mexico
³ Dynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, 47460, Lagos de Moreno, Jalisco, Mexico

^d hgilardi@up.edu.mx

Received: 15 July 2021
Accepted: 16 December 2021
Published online: 3 January 2022

Abstract

In this work, we study the synchronization states for a specific pair of mutually coupled multistable scroll systems. First, we determine conditions in the coupling scheme, to achieve partial or complete synchronization, under a uniform-coupling strength. Second, it is analyzed how the changes in the coupling strength modify the synchronous state. Our main results show that the nature of the coupling scheme determines the obtained synchronization type, while the coupling strength allows us to have various synchronized state attractors that differ from initial attractors. The analysis of the emergence of stable collective behavior is presented using Lyapunov functions of the different couplings and illustrated by numerical simulations.