2013/12/09 by Jesse Berwald, Berwald, Jesse, Marian Gidea +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #37M10 #37M20 #55U99 #68U05 #Chaotic Dynamics (nlin.CD) #Computational Geometry (cs.CG) #Data Analysis #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Statistics and Probability (physics.data-an) #cs.CG #cs.LG #math.DS #msc:37M10 #msc:37M20 #msc:55U99 #msc:68U05 #nlin.CD #physics.data-an
paper · pdf · doi:10.48550/arxiv.1312.2482
arxiv created 2014/03/24 · arxiv updated 2014/03/25
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the system undergoes changes in qualitative behavior. A detailed description of the dynamics can be difficult or impossible to obtain for high-dimensional and chaotic systems. Therefore, a more sensible goal is to recognize and mark transitions of a system between qualitatively different regimes of behavior. In practice, one is interested in developing techniques for detection of such transitions from sparse observations, possibly contaminated by noise. In this paper we develop a framework to accurately tag different regimes of complex systems based on topological features. In particular, our framework works with a high degree of success in picking out a cyclically orbiting regime from a stationary equilibrium regime in high-dimensional stochastic dynamical systems.