Hidden symmetry in networked systems

• Grant number: 24/00930-2
• Support Opportunities: Research Grants - Young Investigators Grants
• Start date: July 01, 2024
• End date: June 30, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Eeltje Cornelis Nijholt
• Grantee: Eeltje Cornelis Nijholt
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 25/05335-8 - Generic Bifurcations in Networks, BP.IC; 25/05370-8 - Branching Lemma for networks, BP.IC; 24/15647-4 - Hidden Symmetries in Networked Systems, BP.JP

Abstract

We will develop mathematical tools for classifying bifurcations and dynamical behavior in network systems. My approach views the network structure as an intrinsic geometrical property, providing a foundation for interdisciplinary techniques. We aim to analyze the impact of interaction structures systematically. The central question in network dynamical systems is the influence of network structure on a dynamical system. This is crucial in various applications, from ecology to power grids, neuroscience to disease control. Despite numerous approaches, some fundamental dynamical systems techniques, especially bifurcation theory, are poorly understood for network systems. Local bifurcations are essential and rich in network systems, yet existing techniques fall short. Addressing this shortcoming is crucial for advancing the field. Our aim goal is to develop a unifying framework based on intrinsic geometrical descriptions to tackle this longstanding open problem (AU)