Research Themes

This research explores the relationship between nonlinear dynamics and partial differential equations (PDEs) as essential tools for understanding complex systems in physics, biology, and networks. We focus on analyzing the time evolution of nonlinear systems with PDEs, examining phenomena such as stability, chaos, and pattern formation. Our aim is to develop a framework for predicting and explaining complex long-term behaviors in both natural and artificial systems. 

This research investigates the interaction between the complex dynamics of the brain and artificial intelligence, providing insights into both biological and artificial intelligence. By analyzing the dynamic mechanisms of neural networks, we aim to apply principles from brain function to AI systems, while deepening our mathematical understanding of brain dynamics. The ultimate goal is to explore the potential convergence of human intelligence and AI.