Summer Undergraduate Research Opportunities in the CHAMPS Project
The breadth and scale of research in CHAMPS provides opportunities for researchers from a variety of backgrounds and levels, even for undergraduates. This summer Wenyang Lyu , an undergraduate in the School of Mathematics at the University of Bristol, personified these characteristics of CHAMPS. Supported by a bursary from the London Mathematical Society and the School of Mathematics, Wenyang completed a research project that will be useful for the CHAMPS project, as well as researchers in related areas worldwide.
Periodic orbits are universally acknowledged as a fundamental building block for phase space structure in dynamical systems. For general nonlinear dynamical systems discovering the existence and nature of periodic orbits can only be carried out using computational methods. For this reason it is important to have numerical methods for fining periodic orbits that lead to reproducible results. Wenyang implemented two know numerical methods for finding periodic orbits in Python, and further developed a new numerical method. He has tested these methods on benchmark two degree-of-freedom Hamiltonian systems.
Wenyang was supervised by Shibabrat Naik, a postdoctoral research associate in the CHAMPS project, and Stephen Wiggins.