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Synchronization of frustrated Kuramoto oscillators on modular networks

Grant number: 23/03917-4
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): May 01, 2023
Effective date (End): April 30, 2025
Field of knowledge:Physical Sciences and Mathematics - Physics
Principal Investigator:Nathan Jacob Berkovits
Grantee:Guilherme Henrique da Silva Costa
Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
Associated research grant:21/14335-0 - ICTP South American Institute for Fundamental Research: a regional center for Theoretical Physics, AP.TEM

Abstract

The emergence of synchronization and its general features are of particular interest to scientists working on several subjects, such as physics, social sciences and biology. From neurons to population dynamics and fireflies, nature showcases several examples of synchronized and collective behavior. In order to understand the basic properties leading to synchronization, Kuramoto proposed a model that became a paradigm in the field, being studied extensively in recent years. Since the original publication of the model in 1975, several extensions and generalizations were proposed, such as replacing the all-to-all coupling to interactions with first neighbors on networks of different topologies, external forces acting on the oscillators, frustration via matrix coupling and higher dimensions.The generalization of the Kuramoto model with coupling matrix proposed by Buzanello and collaborators in 2022 was studied in 2D and in the context of all-to-all interactions. However, in real systems, the elements usually have an interacting neighborhood that can be modeled as a network. Therefore, the study of this model on complex topologies, for example random or scale-free networks, is an interesting open subject that may bring out novel aspects and behaviors regarding synchronization phenomena. A particular topology that draws attention to spreading and synchro-nization phenomena are the modular networks: a collection of nodes organized in groups with the property of being densely connected within the group but interacting weakly with vertices outside the module. Modular networks are interesting substrates to mimic community structure presented in real systems such as neuronal, social and biological networks. Considering the particular case of neuronal networks, another important factor is the effect of external forces driving the oscillators, since the synchronization and spreading of neurons signals are driven by an initial spiking acting on a small portion of neurons. Thus, inspired by the behavior of neuronal synchronization, we intend to study the frustrated Kuramoto model under the influence of external forces on modular networks .

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