Speaker: Hanbaek Lyu (OSU)
Title: Synchronization of finite-state pulse-coupled oscillators
Abstract:
We propose a novel generalized cellular automaton(GCA) model for discrete-time pulse-coupled oscillators and study the emergence of synchrony. Given a finite simple graph and an integer $n\ge 3$, each vertex is an identical oscillator of period $n$ with the following weak coupling along the edges: each oscillator inhibits its phase update if it has at least one neighboring oscillator at a particular "blinking" state and if its state is ahead of this blinking state. We obtain conditions on initial configurations and on network topologies for which states of all vertices eventually synchronize. We show that our GCA model synchronizes arbitrary initial configurations on paths, trees, and with random perturbation, any connected graph. In particular, our main result is the following local-global principle for tree networks: for $n\in \{3,4,5,6\}$, any $n$-periodic network on a tree synchronizes arbitrary initial configuration if and only if the maximum degree of the tree is less than the period $n$. We will also discuss recent results on $\mathbb{Z}$ in relation to annihilating particle systems and random walks, and some interesting conjectures on higher dimensional lattices.
This event is an academic talk by a mathematics graduate student or similarly qualified speaker on their area of research. Members of the organization and other interested parties will be able to attend and hear about the current research of the presenter or some mathematical topic the presenter finds interesting. Attendees are welcome to ask questions and discuss the material.
As always, any student on campus is welcome to attend, regardless of mathematical background.
Note: The purpose of the MGSA is to provide graduate students in the Department of Mathematics the opportunity to interact with each other and present their work to the members and other interested students as well as provide support and encouragement to all mathematics graduate students.
Website: http://mgsa.org.ohio-state.edu