Basins of attraction of chimera states on networks

Qiang Li; Kelly C Larosz; Dingding Han; Peng Ji; Jürgen Kurths

doi:10.3389/fphys.2022.959431

Basins of attraction of chimera states on networks

Front Physiol. 2022 Sep 8:13:959431. doi: 10.3389/fphys.2022.959431. eCollection 2022.

Authors

Qiang Li^{1

2

3}, Kelly C Larosz^{4

5

6}, Dingding Han⁷, Peng Ji^{1

2

3}, Jürgen Kurths^{8

9

10}

Affiliations

¹ Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China.
² Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China.
³ MOE Frontiers Center for Brain Science, Fudan University, Shanghai, China.
⁴ University Center UNIFATEB, Telêmaco Borba, Brazil.
⁵ Graduate Program in Chemical Engineering Federal Technological University of Paraná, Ponta Grossa, Brazil.
⁶ Physics Institute, University of São Paulo, Oscillation Control Group, São Paulo, Brazil.
⁷ School of Information Science and Technology, Fudan University, Shanghai, China.
⁸ Research Institute of Intelligent Complex Systems, Fudan University, Shanghai, China.
⁹ Potsdam Institute for Climate Impact Research, Potsdam, Germany.
¹⁰ Humboldt University, Berlin, Germany.

Abstract

Networks of identical coupled oscillators display a remarkable spatiotemporal pattern, the chimera state, where coherent oscillations coexist with incoherent ones. In this paper we show quantitatively in terms of basin stability that stable and breathing chimera states in the original two coupled networks typically have very small basins of attraction. In fact, the original system is dominated by periodic and quasi-periodic chimera states, in strong contrast to the model after reduction, which can not be uncovered by the Ott-Antonsen ansatz. Moreover, we demonstrate that the curve of the basin stability behaves bimodally after the system being subjected to even large perturbations. Finally, we investigate the emergence of chimera states in brain network, through inducing perturbations by stimulating brain regions. The emerged chimera states are quantified by Kuramoto order parameter and chimera index, and results show a weak and negative correlation between these two metrics.

Keywords: basin stability; brain network; chimera states; complex networks; synchronization patterns.