TY - JOUR
T1 - Cluster Synchronization of Diffusively Coupled Nonlinear Systems
T2 - A Contraction-Based Approach
AU - Aminzare, Zahra
AU - Dey, Biswadip
AU - Davison, Elizabeth N.
AU - Leonard, Naomi Ehrich
N1 - Funding Information:
This work was jointly supported by the National Science Foundation under NSF-CRCNS grant DMS-1430077 and the Office of Naval Research under ONR Grant N00014-14-1-0635. This material is also based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant DGE-1656466. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors thank the anonymous reviewers for their thoughtful and detailed comments.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh–Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.
AB - Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh–Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.
KW - Cluster synchronization
KW - Contraction theory for stability
KW - Diffusively coupled nonlinear networks
KW - Neuronal oscillators
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U2 - 10.1007/s00332-018-9457-y
DO - 10.1007/s00332-018-9457-y
M3 - Article
AN - SCOPUS:85044714285
SN - 0938-8974
VL - 30
SP - 2235
EP - 2257
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
IS - 5
ER -