Hypergraphs in the Study of Critical Transitions and Resilience in Complex Dynamical Systems

• Grant number: 26/03308-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2026
• End date: April 30, 2030
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Fernando Fagundes Ferreira
• Grantee: Ewane Ewane Philippe-Valdes
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated research grant: 25/18142-3 - Study of Resilience and Critical Transitions in Complex Dynamical Systems, AP.R

Abstract

This project proposes a systematic investigation of the dynamics of complex systems with higher-order interactions through hypergraph modeling, combining bifurcation theory, mean-field methods, and analysis of critical transitions. The study will address four interdisciplinary domains: ecology (multiparty competition for resources), econophysics (systemic financial crises), neuroscience (pathological neural synchronization), and sociophysics (opinion dynamics in complex groups). The unified approach will allow the identification of universal principles of resilience and critical transition in systems with non-binary interactions.The theoretical foundation of this project rests on three complementary pillars. First, the theory of dynamic hypergraphs, which generalizes traditional concepts of complex networks to capture multilateral interactions. This approach enables modeling phenomena such as tripartite synapses in the brain (involving pre- and postsynaptic neurons and astrocytes), competition among multiple species for ecological resources, and strategic alliances among financial institutions - all cases where binary interactions are insufficient. Second, the theory of critical transitions and bifurcations adapted to hypergraphs. Here, we will extend the Ott-Antonsen formalism to systems with higher-order couplings, developing master stability functions specific to these topologies. This theoretical extension will allow the identification of critical points and vulnerability zones in systems subject to perturbations, such as ecological collapses or cascading financial crises. Third, mean-field methods will be adapted to deal with the structural heterogeneity of hypergraphs. Through mean-field calculations and Monte Carlo simulations, we will derive effective equations describing the collective behavior of these systems. Statistical mechanics metrics, such as generalized entropy and Kullback-Leibler divergence, will provide quantitative indicators of resilience and proximity to critical transitions. (AU)