Open AccessSynchronization conditions in networks of Hindmarsh-Rose systems
Author(s) -
Sergei A. Plotnikov
Publication year - 2021
Publication title -
cybernetics and physics
Language(s) - English
Resource type - Journals
eISSN - 2226-4116
pISSN - 2223-7038
DOI - 10.35470/2226-4116-2021-10-4-254-259
Subject(s) - rose (mathematics) , synchronization (alternating current) , simple (philosophy) , algebraic number , lyapunov function , control theory (sociology) , computer science , topology (electrical circuits) , mathematics , function (biology) , synchronization networks , mathematical analysis , artificial intelligence , physics , nonlinear system , geometry , combinatorics , philosophy , control (management) , epistemology , quantum mechanics , evolutionary biology , biology
The algebraic connectivity is crucial parameter in studying of synchronization of diffusively coupled networks. This paper studies the synchronization in networks of Hindmarsh-Rose systems, which is one of the most used neuron models. It presents sufficient condition for synchronization in these networks using the Lyapunov function method. This is a simple condition which depends on the algebraic connectivity and on the parameters of the individual system. Numerical examples are presented to illustrate the obtained results.