Controlling cluster synchronization by adapting the topology

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2014-10, Vol.90 (4), p.042914-042914, Article 042914
• Main Authors: Lehnert, Judith, Hövel, Philipp, Selivanov, Anton, Fradkov, Alexander, Schöll, Eckehard
• Format: Article
• Language: English
• Subjects: Algorithms; Fourier Analysis; Models, Theoretical
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/PhysRevE.90.042914

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.