Study of Resilience and Critical Transitions in Complex Dynamical Systems

• Grant number: 25/18142-3
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2026
• End date: January 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Fernando Fagundes Ferreira
• Grantee: Fernando Fagundes Ferreira
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• City of the host institution: Ribeirão Preto
• Associated researchers: Patrick Herve Louodop Fotso ; Thierry Sainclair Njougouo

Abstract

This project proposes a theoretical-computational framework to analyze resilience and critical transitions in complex systems with both pairwise and higher-order interactions. It applies to phenomena such as ecological collapses, neurological crises, and financial instabilities. The proposal is based on three pillars: (1) theoretical development to analyze bifurcations and stability in graphs and hypergraphs, modeling both pairwise and higher-order interactions; (2) the use of machine learning, with recurrent neural networks and reservoir computing, to identify patterns in complex time series; and (3) simulations and active control strategies - such as fixing the state of selected network elements (pinning), automatically adjusting parameters in response to the system's behavior (adaptive feedback), and training algorithms to find solutions through trial and error (reinforcement learning) - aimed at restoring and maintaining the stability of dynamic systems. The tools will be validated using synthetic data and applied to real-world case studies - such as biodiversity collapses, epilepsy, Parkinson's disease, and systemic instabilities. It is expected that this project will contribute to advancing a rigorous, quantitative, and interdisciplinary approach to resilience in complex systems, fostering the development of predictive methods and control strategies applicable across multiple domains. (AU)