THE SCIENCE OF COMPLEX NETWORKS

Eckehard Schöll

Chair Collaborative Research Center SFB 910:

Control of Self-Organizing Nonlinear Systems

Institute for Theoretical Physics

Technische Universität Berlin Germany

http://www.itp.tu-berlin.de/schoell

Centre for Stabilization of Planetary Emergencies Erice 20 August 2016

Control of Planetary Emergences Using the Science of Complex Networks

New Manhattan Project

Examples of complex networks

brain

power grid internet

friendships

Examples of complex networks: transportation

airtraffic

node degree k

roads

node degree k

Examples of complex networks: transportation

airtraffic

node degree k

roads

node degree k

power grid of Northern Italy

Motter et al:

Nature Phys. 9, 191 (2013) transmission lines effective admittances

Synchronization in complex networks

Nonlinear dynamics of complex networks Various synchronization patterns:

● in-phase synchronization (e.g., power grid)

● group/cluster synchronization T. Dahms, J. Lehnert, E. Schöll: Phys. Rev.

E 86, 016202 (2012)

● partial synchronization

5-node network motif:

W. Poel, A. Zakharova, E. Schöll: PRE 91,022915 (2015)

● Chimera states (partially coherent, partially incoherent)

in-phase synchronization

amplitude death

antiphase synchronization

Control of chimeras

Control of chimeras in small networks

I.Omelchenko,O.Omelchenko,A.Zakharova,M.Wolfrum,E.Schöll: PRL 116,114101(2016)

Small networks: short lifetime, erratic drifting of incoherent domain

Idea: combine symmetric and asymmetric feedback control to increase

lifetime and fix position - tweezers for chimeras in small networks

Van der Pol oscillator with asymmetric coupling:

right/left order parameters

Control of chimeras in small networks

N=24

N=12

I. Omelchenko, O. Omelchenko, A. Zakharova, M. Wolfrum, E.Schöll: PRL 116 (2016)

Mathematics Physics

Computer

Science

● interdisciplinary

● theoretically oriented ● concepts of application

● development of methods

Nonlinear

dynamics,

control

Collaborative Research Center SFB 910 Control of Self-Organizing Nonlinear Systems:

Theoretical Methods and Concepts of Application

17 projects, 21 PIs

(Berlin, Saratov/Russia)

funded by German Research

Foundation (DFG) since 2011

Annual Budget from DFG:

2.25 Mio EUR

International conferences organized by the SFB 910

2012 Palma de Mallorca 2014 Warnemünde September 2016 Usedom Delayed Complex Systems (DCS12) attended by 110 scientists from 14 countries

Conference Activities

International networking

External Collaborations

B1:Fainstein

A4:Satou,

Nakayama

B1:Benson

B2:von Klitzing

B8:Bankenburg

B9:Bimberg

B10:Selhorst

A3:Giacomelli

A1:Jiruska

B2:Yellen

B1:Vos

A1:Krischer, A3:Tass, A4,B5,B6:Hauser

A7:Haug,Oberthaler, B1:Benson

B2:von Klitzing, B4:Wagner, B5:Käs,Luther

B8:Blankenburg,Logothetis

B9:Bimberg, B10:Selhorst

A7: Haug

A3:Tass

B5:Käs

B8:Logothetis

B5:Luther

A7:Oberthaler

B2:Wagner

A4,B5,B6:

Hauser

A3:Kapitaniak

B6:Steinbock

B10:Barabasi,

Ratti B9:Grillot

A3,B9:Fischer A1:Roy

B4:Cicuta

A1,B6:Showalter

A1,A3:Gauthier

B4:Di Carlo

A1:Anishchenko,

Vadivasova

B9:Kelleher

Concepts of control - different approaches:

• nonlinear dynamics and chaos control

• classical control theory

• quantum control

Fields of application - selected innovative systems:

• Control of networks

• Control of quantum nanostructures

• Control of soft condensed matter and microfluidics

• Control of active media and biological systems

Central and Connecting Scientific Aims

Control Concepts

● Control of nonlinear dynamic systems

● Classical control and optimization

● Coherent quantum control

Closed loop control (feedback control)

adaptability

robustness

reduced sensitivity to model uncertainties

state vector

control variable

output variable

Control concepts

● Small self-adaptable control force allows us to stabilize different patterns

● Various applications of time-delayed feedback, e.g. to robotic control (Steingrube et al., Nature Physics 2010)

Pyragas control

Design and Control of Nonlinear Dynamics in Complex Networks

● time-delayed dynamics

● external forces and fields

● feedback loops and couplings

Interdisciplinary: methodical common features in systems of very different nature micro/macro world, classical/quantum, socio-economics

● spatio-temporal pattern selection

● manipulation – self-organization

● stabilization of unstable states

Ubiquitous Methodical Concepts ● Interaction of coupled elements, with and without delay

● Dynamics and interaction on competing time scales

● Multiple space scales from nano via micro to macro

● Dynamics on and of networks: adaptive networks

● Symmetry-breaking: partial synchronization, chimera states

● Stochastic effects: e.g., fluctuating wind engines in smart grids with renewable energies

● Heterogeneous networks, complex topologies (small world, fractal, hierarchical, multi-partite, multilayer)

Interplay of dynamics, structure, noise, delay

τ2 τ1

Literature 2016

● A.Motter et al: Nature Phys. 9, 191 (2013)

● V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, Phys. Rev. Lett. 105, 254101 (2010).

● I. Omelchenko, Maistrenko, Hövel, and E. Schöll, Phys. Rev. Lett. 106, 234102 (2011).

● A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. I. Omelchenko, E. Schöll:, Nature Phys. 8, 658 (2012).

● I. Omelchenko, O.Omel’chenko, P.Hövel, E. Schöll: When Phys. Rev. Lett. 110, 224101 (2013).

● A. Zakharova, M. Kapeller, and E. Schöll, Phys. Rev. Lett. 112, 154101 (2014).

● I.Omelchenko,O.Omel’chenko,A.Zakharova,M.Wolfrum E. Schöll, Phys. Rev. Lett. 116, 114101 (2016)

● N.Semenova, A.Zakharova, V.S. Anishchenko E.Schöll, Phys. Rev. Lett. 117, 014102 (2016)

● E. Schöll, EPJ-ST (Sept. 2016) Special Theme Issue on Complex Systems (T.Bountis)