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Adaptive control of cluster synchronization in delay-coupled networks

Philipp Hoevel, Judith Lehnert, Eckehard Schöll, Anton Selivanov, Alexander Fradkov
Adaptive control methods are useful in situations where parameters are
unknown or drift as they allow for automatically tuning the parameters
to appropriate values. They are, therefore, of particular interest for
experiments and technological applications. Here, we develop two
adaptive control schemes for the control of zero-lag and cluster
synchronization in delay-coupled Stuart-Landau oscillators which are
generic for systems close to a Hopf bifurcation. The first method
relies on the adaptation of the phase of the complex coupling
strength, while for the second method we adapt the topology of the
network in order to reach the target state. In both cases, we derive
the adaptive controller by using the speed-gradient method.
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