Normal forms and centre manifold reductions for networks

• Grant number: 20/01100-2
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): November 01, 2021
• Effective date (End): October 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal researcher: Tiago Pereira da Silva
• Grantee: Eeltje Cornelis Nijholt
• Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

A network encodes a structure of individual units (the nodes), together with the information of how these units depend on each other. We project focus on qualitative changes in the dynamics of networks as one or more parametersvary. One can, for example, think about the emergence of steady state points or periodic orbits, or the phenomenon whereby multiple cells in a network start displaying identical dynamical behaviour (synchronisation). Due to the nature of network structures, thesymmetries are often more "exotic" than compact groups;equivariance of a dynamical system will often mean with respect to theaction of a finite monoid (i.e. a group without inverses) and therepresentations in question will often be of semigroups. The project deals with such normal form reduction to understand how collectivedynamics appear with such systems. (AU)