Synchronization in random heterogeneous networks

• Grant number: 15/08958-4
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2015
• End date: July 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Tiago Pereira da Silva
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Recent results have revealed that typical networks have multiple scales characterised by different levels of connectivity. These heterogeneous networks exhibit synchronised dynamics at various connectivity scales. Striking examples are found in the brain, where synchronisation between highly connected neurons shapes the network. These important synchronisation phenomena are high-dimensional and are vastly unexplored phenomenon. The major challenge is to develop dimension reduction principles at different network scales that allow the description of the synchronisation.The goal of this proposal is to establish a research group to lead the development of a theory for synchronisation in heterogeneous networks. I aim at following objective:(1) The development of reduction principles to describe the synchronisation dynamics at various levels at connectivity. I aim at establishing a probabilistic theory to provide a low-dimensional description for synchronisation phenomena in terms of the network's microscopic details. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

TANZI, MATTEO; PEREIRA, TIAGO; VAN STRIEN, SEBASTIAN. Robustness of ergodic properties of non-autonomous piecewise expanding maps. Ergodic Theory and Dynamical Systems, v. 39, n. 4, p. 1121-1152, APR 2019. (15/08958-4)

MAIA, DANIEL M. N.; MACAU, ELBERT E. N.; PEREIRA, TIAGO. Persistence of Network Synchronization under Nonidentical Coupling Functions. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 15, n. 3, p. 1563-1580, 2016. (15/08958-4, 11/50151-0)

TANZI, MATTEO; PEREIRA, TIAGO; VAN STRIEN, SEBASTIAN. Robustness of ergodic properties of non-autonomous piecewise expanding maps. Ergodic Theory and Dynamical Systems, v. 39, p. 32-pg., 2019-04-01. (15/08958-4)