Rafael Obaya Garcia

Rafael Obaya Garcia is a Professor in the Department of Applied Mathematics at the University of Valladolid, specializing in Dynamical Systems theory. His research focuses on nonautonomous differential equations, bifurcation theory, and critical transitions with applications in mathematical ecology and engineering systems. He leads significant research projects and has built an extensive publication record that includes over 100 journal articles, 5 books, and 13 book chapters.

His primary research interests center on nonautonomous dynamical systems, particularly focusing on d-concave systems, critical transitions, and bifurcation theory. His work bridges pure mathematical theory with practical applications in ecological modeling, population dynamics, and circuit theory. He has developed important theoretical frameworks for understanding rate-induced transitions and saddle-node bifurcations in nonautonomous contexts, contributing significantly to the mathematical understanding of resilience and regime shifts in complex systems.

Analysis of his recent publications reveals a strong focus on critical transitions in nonautonomous systems, particularly examining d-concave differential equations. His work connects theoretical dynamical systems with practical ecological applications, showing how mathematical frameworks can predict and explain regime shifts in natural systems. He has established important connections between bifurcation theory, stability analysis, and ecological resilience, demonstrating how mathematical structures underpin critical transitions in real-world systems.

Professor Obaya leads the research project "NON-AUTONOMOUS DYNAMICS METHODS WITH APPLICATION IN THE STUDY OF CRITICAL TRANSITIONS" (PID2021-125446NB-I00, 2022-2025), funded by the State Research Agency, ERDF Funds, European Union, and MICINN. He has supervised doctoral students including Jesus Dueñas Pamplona, whose thesis focused on "D-concave nonautonomous differential equations and applications to critical transitions." His research group includes Ana Maria Sanz, Maria del Carmen Núñez, Sylvia Novo, and Victor Muñoz Villarragut.

He is actively involved in the research community through conference organization, including the "Dynamical Systems, Nonautonomous Differential Equations, and Critical Transitions Meeting" in Valladolid (2025), and has participated in international collaborations such as the "INTEGRATED ACTION WITH HUNGARY 2009-2011" on functional differential equations. His work demonstrates a strong commitment to advancing both theoretical mathematics and its applications to real-world complex systems.