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Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling

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Maia,  Daniel
External Organizations;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

/persons/resource/yanchuk

Yanchuk,  Serhiy
Potsdam Institute for Climate Impact Research;

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Maia, D., Kurths, J., Yanchuk, S. (2023): Stabilization of synchronous equilibria in regular dynamical networks with delayed coupling. - Nonlinear Dynamics, 111, 7377-7390.
https://doi.org/10.1007/s11071-022-08220-w


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We consider the synchronization problem of dynamical networks with delayed interactions. More specifically, we focus on the stabilization of synchronous equilibria in regular networks where the degrees of all nodes are equal. By studying such control near a Hopf bifurcation, we obtain necessary and sufficient conditions for stabilization. It is shown that the stabilization domains in the parameter space reappear periodically with time-delay. We find that the frequency of reappearance of the control domains is linearly proportional to the number of cycle multipartitions of the network.