Controlling cluster synchronization by adapting the topology.
We suggest an adaptive control scheme for the control of in-phase and cluster synchronization in delay-coupled networks. Based on the speed-gradient method, our scheme adapts the topology of a network such that the target state is realized. It is robust towards different initial conditions as well as changes in the coupling parameters. The emerging topology is characterized by a delicate interplay of excitatory and inhibitory links leading to the stabilization of the desired cluster state. As a crucial parameter determining this interplay we identify the delay time. Furthermore, we show how to construct networks such that they exhibit not only a given cluster state but also with a given oscillation frequency. We apply our method to coupled Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in an expansion of systems close to a Hopf bifurcation. The successful and robust control of this generic model opens up possible applications in a wide range of systems in physics, chemistry, technology, and life science.
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
Judith
J
Lehnert
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany and Bernstein Center for Computational Neuroscience, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany.
Philipp
P
Hövel
Department of Theoretical Cybernetics, Saint-Petersburg State University, Saint-Petersburg, Russia.
Anton
A
Selivanov
Department of Theoretical Cybernetics, Saint-Petersburg State University, Saint-Petersburg, Russia and Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoy Avenue, 61, Vasilievsky Ostrov, St. Petersburg, 199178 Russia.
Alexander
A
Fradkov
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
Eckehard
E
Schöll
D000465:Algorithms; D005583:Fourier Analysis; D008962:Models, Theoretical