1
|
Bayani A, Nazarimehr F, Jafari S, Kovalenko K, Contreras-Aso G, Alfaro-Bittner K, Sánchez-García RJ, Boccaletti S. The transition to synchronization of networked systems. Nat Commun 2024; 15:4955. [PMID: 38858358 PMCID: PMC11165003 DOI: 10.1038/s41467-024-48203-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 04/23/2024] [Indexed: 06/12/2024] Open
Abstract
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network's nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems.
Collapse
Affiliation(s)
- Atiyeh Bayani
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
| | - Fahimeh Nazarimehr
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
- Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
| | - Kirill Kovalenko
- Scuola Superiore Meridionale, School for Advanced Studies, Naples, Italy
| | | | | | - Rubén J Sánchez-García
- Mathematical Sciences, University of Southampton, Southampton, UK.
- Institute for Life Sciences, University of Southampton, Southampton, UK.
- The Alan Turing Institute, London, UK.
| | - Stefano Boccaletti
- CNR - Institute of Complex Systems, Sesto Fiorentino, Italy
- Sino-Europe Complexity Science Center, School of Mathematics, North University of China, Shanxi, Taiyuan, China
- Research Institute of Interdisciplinary Intelligent Science, Ningbo University of Technology, Zhejiang, Ningbo, China
| |
Collapse
|
2
|
Nag Chowdhury S, Anwar MS, Ghosh D. Cluster formation due to repulsive spanning trees in attractively coupled networks. Phys Rev E 2024; 109:044314. [PMID: 38755838 DOI: 10.1103/physreve.109.044314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2023] [Accepted: 03/22/2024] [Indexed: 05/18/2024]
Abstract
Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological processes. The current literature has investigated cluster synchronization by focusing mostly on the case of attractive coupling among the oscillators. However, the case of two coexisting competing interactions is of practical interest due to their relevance in diverse natural settings, including neuronal networks consisting of excitatory and inhibitory neurons, the coevolving social model with voters of opposite opinions, and ecological plant communities with both facilitation and competition, to name a few. In the present article, we investigate the impact of repulsive spanning trees on cluster formation within a connected network of attractively coupled limit-cycle oscillators. We successfully predict which nodes belong to each cluster and the emergent frustration of the connected networks independent of the particular local dynamics at the network nodes. We also determine local asymptotic stability of the cluster states using an approach based on the formulation of a master stability function. We additionally validate the emergence of solitary states and antisynchronization for some specific choices of spanning trees and networks.
Collapse
Affiliation(s)
- Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, Davis, California 95616, USA
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Md Sayeed Anwar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| |
Collapse
|
3
|
Baruzzi V, Lodi M, Sorrentino F, Storace M. Bridging functional and anatomical neural connectivity through cluster synchronization. Sci Rep 2023; 13:22430. [PMID: 38104227 PMCID: PMC10725511 DOI: 10.1038/s41598-023-49746-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 12/11/2023] [Indexed: 12/19/2023] Open
Abstract
The dynamics of the brain results from the complex interplay of several neural populations and is affected by both the individual dynamics of these areas and their connection structure. Hence, a fundamental challenge is to derive models of the brain that reproduce both structural and functional features measured experimentally. Our work combines neuroimaging data, such as dMRI, which provides information on the structure of the anatomical connectomes, and fMRI, which detects patterns of approximate synchronous activity between brain areas. We employ cluster synchronization as a tool to integrate the imaging data of a subject into a coherent model, which reconciles structural and dynamic information. By using data-driven and model-based approaches, we refine the structural connectivity matrix in agreement with experimentally observed clusters of brain areas that display coherent activity. The proposed approach leverages the assumption of homogeneous brain areas; we show the robustness of this approach when heterogeneity between the brain areas is introduced in the form of noise, parameter mismatches, and connection delays. As a proof of concept, we apply this approach to MRI data of a healthy adult at resting state.
Collapse
Affiliation(s)
| | - Matteo Lodi
- DITEN, University of Genoa, Via Opera Pia 11a, 16145, Genova, Italy
| | - Francesco Sorrentino
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM, 87131, USA
| | - Marco Storace
- DITEN, University of Genoa, Via Opera Pia 11a, 16145, Genova, Italy.
| |
Collapse
|
4
|
Zhang L, Pan W, Yan L, Luo B, Zou X, Li S. Hierarchical-dependent cluster synchronization in directed networks with semiconductor lasers. OPTICS LETTERS 2022; 47:5108-5111. [PMID: 36181198 DOI: 10.1364/ol.471943] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Accepted: 09/11/2022] [Indexed: 06/16/2023]
Abstract
Cluster synchronization in complex networks with mutually coupled semiconductor lasers (SLs) has recently been extensively studied. However, most of the previous works on cluster synchronization patterns have concentrated on undirected networks. Here, we numerically study the complete cluster synchronization patterns in directed networks composed of SLs, and demonstrate that the values of the SLs parameter and network parameter play a prominent role on the formation and stability of cluster synchronization patterns. Moreover, it is shown that there is a hierarchical dependency between the synchronization stability of different clusters in directed networks. The stability of one cluster can be affected by another cluster, but not vice versa. Without loss of generality, the results are validated in another SLs network with more complex topology.
Collapse
|
5
|
Panahi S, Klickstein I, Sorrentino F. Cluster synchronization of networks via a canonical transformation for simultaneous block diagonalization of matrices. CHAOS (WOODBURY, N.Y.) 2021; 31:111102. [PMID: 34881582 DOI: 10.1063/5.0071154] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
We study cluster synchronization of networks and propose a canonical transformation for simultaneous block diagonalization of matrices that we use to analyze the stability of the cluster synchronous solution. Our approach has several advantages as it allows us to: (1) decouple the stability problem into subproblems of minimal dimensionality while preserving physically meaningful information, (2) study stability of both orbital and equitable partitions of the network nodes, and (3) obtain a parameterization of the problem in a small number of parameters. For the last point, we show how the canonical transformation decouples the problem into blocks that preserve key physical properties of the original system. We also apply our proposed algorithm to analyze several real networks of interest, and we find that it runs faster than alternative algorithms from the literature.
Collapse
Affiliation(s)
- Shirin Panahi
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Isaac Klickstein
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Francesco Sorrentino
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| |
Collapse
|