Description:

P&A Complex Systems Seminar

Judith Lehnert

Institute for Theoretical Physics

Berlin Technical University

Control of Complex Networks: Interplay of Dynamics and Topology

Studies of complex networks have sparked tremendous scientic activities in many research areas ranging from Physics, Biology, and Chemistry to Social Sciences. One of the central topics of dynamics on networks is synchronization which is observed in very different contexts[1], for example, in genetic oscillators, population dynamics, neural populations, wireless communication, or opinion formation. Our work aims for a fundamental understanding of synchronization, its control, and its interplay with the topology of complex networks. Besides considering the existence and stability of complex synchronization states [2, 3], I will focus in this talk on adaptive control methods, which allow for controlling synchronization in scenarios where parameters drift or are unknown. These methods are, therefore, of particular interest for experimental setups or technological applications. Here, I will consider 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 [4, 6]. Furthermore, I will consider synchronization and its control in the present of heterogeneities [7, 8], which are known to hinder synchronization.

References:
[1] A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Rep. 469, 93 (2008).
[2] J. Lehnert, T. Dahms, P. Hövel, and E. Schöll, Europhys. Lett. 96, 60013 (2011).
[3] T. Dahms, J. Lehnert, and E. Schöll, Phys. Rev. E 86, 016202 (2012).
[4] A. A. Selivanov, J. Lehnert, T. Dahms, P. Hövel, A. L. Fradkov, and E. Schöll, Phys. Rev. E 85, 016201 (2012).
[5] J. Lehnert, P. Hövel, A. A. Selivanov, A. L. Fradkov, and E. Schöll, Phys. Rev. E 90, 042914 (2014).
[6] P. Hövel, J. Lehnert, A. Selivanov, A. L. Fradkov, and E. Schöll, in Control of Self-Organizing Nonlinear Systems, edited by E. Schöll, S. H. L. Klapp, and P. Hövel (Springer, Berlin, Heidel-berg, 2016).
[7] C. Cakan, J. Lehnert, and E. Schöll, Eur. Phys. J. B 87, 54 (2014).
[8] S. A. Plotnikov, J. Lehnert, A. L. Fradkov, and E. Schöll, Int. J. Bifur. Chaos (2016), arXiv:1503.07657v1.