Dynamical Characterization of Complex Heterogeneous Networks: Synchronization and Beyond

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Several real social, biological, and technological systems can be described as sets of individual components or nodes coupled by connections to form a "network." These networks are denoted as heterogeneous if they are characterized by nodes and connections with different individual properties. Heterogeneity is typical of many natural networks; for example, neuronal networks are characterized by different types of neurons and connections between them. Understanding how heterogeneity affects the network functions may enhance our ability to design and interact with complex dynamical systems that can be described as networks as found in various technological applications. These include swarms of vehicles, robots, smart grids among others. A large body of literature has studied how the structure of these networks affects their dynamic behavior. However, the role of heterogeneous nodes and connections has not been fully investigated. In this project, the PI will investigate synchronization as a dynamic process where the nodes of heterogeneous networks converge on a common time evolution. The dynamic behavior of heterogeneous networks will also be considered in other contexts, including the study of robotic networks composed of ground and aerial vehicles, as well as smart grids and evolutionary game theory for agents interacting over a network.This research will impact the current knowledge and understanding of complex systems by explicitly taking into account their heterogeneous features, which in turn will provide a more detailed characterization of these systems and a better insight into their potential applications. A low dimensional approach to the characterization of the dynamics of these systems will consist of a reduced number of equations that describe the overall dynamics of the network and its stability. Tools from the theory of nonlinear dynamics will be employed to analyze the conditions for the emergence of fixed points, limit cycles and chaotic dynamics in the networks under consideration. In addition, a simple and intuitive online applet will be developed that will allow users to upload a given heterogeneous network and will output an analysis of its dynamical features in real time. This will provide a valuable tool to other researchers who work with social, technological, physical, and biological networks of the kind investigated herein. The applet will also be used to expose a broader audience to the fascinating dynamical properties of the complex heterogeneous networks examined in this study, to their unique characteristics, and to the exciting implications of the findings discussed herein for a number of scientific and engineering fields.