TY - JOUR
T1 - Windows of opportunity for synchronization in stochastically coupled maps
AU - Golovneva, Olga
AU - Jeter, Russell
AU - Belykh, Igor
AU - Porfiri, Maurizio
N1 - Funding Information:
This work was supported by the US Army Research Office under Grant No. W911NF-15-1-0267 with Drs. Samuel C. Stanton and Alfredo Garcia as the program managers.
PY - 2017/2/1
Y1 - 2017/2/1
N2 - Several complex systems across science and engineering display on–off intermittent coupling among their units. Most of the current understanding of synchronization in switching networks relies on the fast switching hypothesis, where the network dynamics evolves at a much faster time scale than the individual units. Recent numerical evidence has demonstrated the existence of windows of opportunity, where synchronization may be induced through non-fast switching. Here, we study synchronization of coupled maps whose coupling gains stochastically switch with an arbitrary switching period. We determine the role of the switching period on synchronization through a detailed analytical treatment of the Lyapunov exponent of the stochastic dynamics. Through closed-form expressions and numerical findings, we demonstrate the emergence of windows of opportunity and elucidate their nontrivial relationship with the stability of synchronization under static coupling. Our results are expected to provide a rigorous basis for understanding the dynamic mechanisms underlying the emergence of windows of opportunity and leverage non-fast switching in the design of evolving networks.
AB - Several complex systems across science and engineering display on–off intermittent coupling among their units. Most of the current understanding of synchronization in switching networks relies on the fast switching hypothesis, where the network dynamics evolves at a much faster time scale than the individual units. Recent numerical evidence has demonstrated the existence of windows of opportunity, where synchronization may be induced through non-fast switching. Here, we study synchronization of coupled maps whose coupling gains stochastically switch with an arbitrary switching period. We determine the role of the switching period on synchronization through a detailed analytical treatment of the Lyapunov exponent of the stochastic dynamics. Through closed-form expressions and numerical findings, we demonstrate the emergence of windows of opportunity and elucidate their nontrivial relationship with the stability of synchronization under static coupling. Our results are expected to provide a rigorous basis for understanding the dynamic mechanisms underlying the emergence of windows of opportunity and leverage non-fast switching in the design of evolving networks.
KW - Networks
KW - Stochastic stability
KW - Switching
KW - Synchronization
KW - Windows of opportunity
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U2 - 10.1016/j.physd.2016.08.005
DO - 10.1016/j.physd.2016.08.005
M3 - Article
AN - SCOPUS:84999810208
VL - 340
SP - 1
EP - 13
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
ER -