Theoretical and Computational Studies of Emergence in Nonlinear Systems
Thomas Antonsen | email
The conceptual simplicity of many problems in nonlinear dynamics makes them readily accessible to undergraduate researchers who wish to pursue theoretical/computational research.
TREND students working on the emergence of global patterns in nonlinear systems will be directed jointly by Professors Girvan, Ott, and Antonsen (or some subset thereof) and aided by a graduate student. Examples of this group's current research activities that are especially studied for undergraduate participation include:
- Development of new numerical techniques for the study of chaotic dynamics (e.g., for studying chaotic scattering, basins of attraction, transient chaos, etc.)
- Exploration of the dynamics of networks of interconnected elements, with applications to biological and technological systems
- investigations of synchronization in chaotic systems
- exploration of machine learning techniques for the prediction of chaotic dynamics
Undergraduates working on these kinds of projects will gain skills in areas such as asymptotic analysis and numerical simulation.
Examples of past undergraduate projects, all resulting in published papers, include the following: a study of how a periodic pacing signal influences the transition from the unsynchronized to the synchronized state in large systems of couple oscillators; a study of the path to synchronization in systems of coupled oscillators with complex network topology; and a study of an abrupt or "explosive" connectivity transition in grouping networks when links are added competitively.
Professors Girvan, Ott, and Antonsen have mentored well over a dozen TREND students, resulting in numerous publications.