Controlled synchronization in heterogeneous multilayer networks

• Applicant: Professor Dr. Eckehard Schöll
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 429685422

• Final Report Year: 2025

Final Report Abstract

The objectives of the present project were to investigate partial synchronization patterns like chimera states or solitary states and relay synchronization in complex networks, as well as to reveal the possibilities and methods of controlling the synchronization of the spatio-temporal dynamics of complex systems. We showed that control can be achieved, e.g., by relay synchronization of the outer layers of a three-layer network via the middle layer which can be reduced to a single node (a hub), or by input of external signals (sound, music) into the auditory cortex of a brain network, or by adaptivity of the link weights, or by time-varying ”blinking” coupling functions which determine which dynamic variables of different nodes are connected with each other, or by coupling delay, or by the effect of noise. Chimera states are characterized by the spatial coexistence of domains of synchronized and desynchronized dynamics, while solitary states are scenarios where all nodes except a few isolated nodes are synchronized. Our focus was on applications to brain networks, and to physiological networks including the immune system, and to a socio-economic model of business cycles. The brain networks were modeled by paradigmatic FitzHugh-Nagumo dynamics on the nodes and empirical network connectivities obtained from diffusion-weighted magnetic resonance imaging (MRI). The physiological networks were described by a two-layer network model (organ layer and immune layer) of adaptively coupled phase oscillators, with co-evolutionary dynamics of organ cells, immune cells, and cytokines mediating the adaptive interactions, resulting in either a healthy fully frequency synchronized state, or a pathological two-frequency cluster state. In the socio-economic model economic shocks are caused by the decisions of a few agents who have a disproportionate influence over the macroscopic state of the economy due to the unequal distribution of wealth among the population.

Publications

• Influence of Sound on Empirical Brain Networks. Frontiers in Applied Mathematics and Statistics, 7.
  Sawicki, Jakub & Schöll, Eckehard
  
• Partial synchronization patterns in brain networks. Europhysics Letters, 136(1), 18001.
  Schöll, Eckehard
  
• Synchronization scenarios in three-layer networks with a hub. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(7).
  Sawicki, Jakub; Koulen, Julia M. & Schöll, Eckehard
  
• Blinking coupling enhances network synchronization. Physical Review E, 105(5).
  Parastesh, Fatemeh; Rajagopal, Karthikeyan; Jafari, Sajad; Perc, Matjaž & Schöll, Eckehard
  
• Controlling chimera and solitary states by additive noise in networks of chaotic maps. Journal of Difference Equations and Applications, 29(9-12), 909-930.
  Rybalova, Elena; Schöll, Eckehard & Strelkova, Galina
  
• Critical Parameters in Dynamic Network Modeling of Sepsis. Frontiers in Network Physiology, 2.
  Berner, Rico; Sawicki, Jakub; Thiele, Max; Löser, Thomas & Schöll, Eckehard
  
• Editorial: Network Physiology, Insights in Dynamical Systems: 2021. Frontiers in Network Physiology, 2.
  Schöll, Eckehard
  
• Introduction to focus issue: In memory of Vadim S. Anishchenko: Statistical physics and nonlinear dynamics of complex systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(1).
  Zakharova, Anna; Strelkova, Galina; Schöll, Eckehard & Kurths, Jürgen
  
• Modeling Tumor Disease and Sepsis by Networks of Adaptively Coupled Phase Oscillators. Frontiers in Network Physiology, 1.
  Sawicki, Jakub; Berner, Rico; Löser, Thomas & Schöll, Eckehard
  
• Modelling the perception of music in brain network dynamics. Frontiers in Network Physiology, 2.
  Sawicki, Jakub; Hartmann, Lenz; Bader, Rolf & Schöll, Eckehard
  
• Perspectives on adaptive dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(7).
  Sawicki, Jakub; Berner, Rico; Loos, Sarah A. M.; Anvari, Mehrnaz; Bader, Rolf; Barfuss, Wolfram; Botta, Nicola; Brede, Nuria; Franović, Igor; Gauthier, Daniel J.; Goldt, Sebastian; Hajizadeh, Aida; Hövel, Philipp; Karin, Omer; Lorenz-Spreen, Philipp; Miehl, Christoph; Mölter, Jan; Olmi, Simona; Schöll, Eckehard ... & Kurths, Jürgen
  
• Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(7).
  Bukh, A. V.; Shepelev, I. A.; Elizarov, E. M.; Muni, S. S.; Schöll, E. & Strelkova, G. I.
  
• Interplay of synchronization and cortical input in models of brain networks. Europhysics Letters, 146(4), 41001.
  Sawicki, Jakub & Schöll, Eckehard
  
• Macroscopic Stochastic Model for Economic Cycle Dynamics. Physical Review Letters, 134(4).
  Nagel, Sören; Heitzig, Jobst & Schöll, Eckehard