A combinatorial/algebraic topological approach to nonlinear dynamics
Time and place
12:30 PM on Thursday, March 28th, 2019; NAC 6/114
Konstantin Mischaikow (Rutgers U.)
Abstract
Motivated by the increase in data driven science I will discuss a combinatorial/algebraic topological approach to characterizing nonlinear dynamics. In particular, I will describe how order theory can be used to efficiently and effectively organize the decomposition of dynamics and how algebraic topological tools can be used to characterize the structure of the dynamics. I will then propose a definition of nonlinear dynamics based on these structures. To demonstrate the effectiveness of this approach I will consider several problems from systems and synthetic biology. I will focus on identification and rejection of network models for these types of systems based on functional form and time series data.
