Necessary and sufficient conditions for identical synchronization in a network of two ordinary diferential systems of Hindmarsh-Rose 3D type with bidirectionally linear coupling

Abstract

This study explores the sufficient and necessary conditions for achieving identical synchronization in a network of two ordinary differential systems of Hindmarsh-Rose 3D type (HR) with bidirectionally linear coupling. By constructing a suitable Lyapunov function, sufficient conditions are identified, while necessary conditions are derived using the largest transverse Lyapunov exponent. The findings indicate that identical synchronization occurs only when the coupling strength is sufficiently large. Additionally, this study employs numerical methods implemented in the R software to test the concerned theories.