The Lyapunov-Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

Author(s)

Grzybowski, J. M. V. ; Macau, E. E. N. ; Yoneyama, T.

• Document type: Journal article
• Source: PHYSICA D-NONLINEAR PHENOMENA; v. 346, p. 28-36, MAY 1 2017.
• Web of Science Citations: 1

Abstract

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rossler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron. (C) 2017 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants