TY - GEN
T1 - Synchronization bound for networks of nonlinear oscillators
AU - Davison, Elizabeth N.
AU - Dey, Biswadip
AU - Leonard, Naomi Ehrich
N1 - Funding Information:
This research was supported in part by the Office of Naval Research under ONR grant N00014-14-1-0635 and by the National Science Foundation under Grant No. DGE-1656466
Publisher Copyright:
© 2016 IEEE.
PY - 2017/2/10
Y1 - 2017/2/10
N2 - Investigation of synchronization phenomena in networks of coupled nonlinear oscillators plays a pivotal role in understanding the behavior of biological and mechanical systems with oscillatory properties. We derive a general sufficient condition for synchronization of a network of nonlinear oscillators using a nonsmooth Lyapunov function, and we obtain conditions under which synchronization is guaranteed for a network of Fitzhugh-Nagumo (FN) oscillators in biologically relevant model parameter regimes. We incorporate two types of heterogeneity into our study of FN oscillators: 1) the network structure is arbitrary and 2) the oscillators have non-identical external inputs. Understanding the effects of heterogeneities on synchronization of oscillators with inputs provides a promising step toward control of key aspects of networked oscillatory systems.
AB - Investigation of synchronization phenomena in networks of coupled nonlinear oscillators plays a pivotal role in understanding the behavior of biological and mechanical systems with oscillatory properties. We derive a general sufficient condition for synchronization of a network of nonlinear oscillators using a nonsmooth Lyapunov function, and we obtain conditions under which synchronization is guaranteed for a network of Fitzhugh-Nagumo (FN) oscillators in biologically relevant model parameter regimes. We incorporate two types of heterogeneity into our study of FN oscillators: 1) the network structure is arbitrary and 2) the oscillators have non-identical external inputs. Understanding the effects of heterogeneities on synchronization of oscillators with inputs provides a promising step toward control of key aspects of networked oscillatory systems.
KW - Complex Networked Systems
KW - Lyapunov Analysis
KW - Nonlinear Oscillators
KW - Synchronization
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U2 - 10.1109/ALLERTON.2016.7852359
DO - 10.1109/ALLERTON.2016.7852359
M3 - Conference contribution
AN - SCOPUS:85015239563
T3 - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
SP - 1110
EP - 1115
BT - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
Y2 - 27 September 2016 through 30 September 2016
ER -