The first main area involves the question of whether it is possible, even in principle, for long-term computer simulations of typical nonhyperbolic chaotic systems to approximately match true system behavior. Part of this research involves developing quantitative laws of the expected waiting time between breakdowns, or mismatches, between computer simulation trajectories and the trajectories of computer models. . The second major area is ongoing work by the investigator on the interpretation of physical and biological experiments that generate aperiodic time series. Using univariate or multivariate time series or inter-event time intervals produced by a deterministic physical process, the phase space of the process can be faithfully reconstructed as the basis for applications such as system identification, filtering, prediction and control. Topological and diffeomorphic embedding theorems guaranteeing this in various physically verifiable contexts have been the results of previous and ongoing research by the investigator and coworkers.
Computer simulations are a staple of modern science.
National policy decisions are being made which rely partially on the interpretation of long-term computer . . . More on THIS Work .