Research Projects

This project aims to design a mathematical framework for dynamical networks of mixed dynamics, predicting emergent spatiotemporal patterns and scaling patterns in Jacobian ensembles and predicting the stability of such networks. Previous research has focused on finding dynamic exponents to find scaling patterns in the Jacobian matrix and predicting system stability. However, this proposal focuses on developing a theory for networks that considers mixed dynamics on nodes and links, mimicking the actual process of more realistic systems. The proposal aims to leverage theoretical understanding of network dynamics, developed through systematic translation of topological characteristics, dynamical behavior, and spatiotemporal patterns, into practical dynamic stability of a network of mixed dynamics. If successful, this work will advance the understanding of the dynamical framework and behavior of mixed dynamics or more realistic systems, provide a theoretical framework to observe emergent patterns in mixed dynamical networks, and predict their stability.