Chaos in Higher Dimensions

Drexel University, Philadelphia PA

Investigators

Abstract

9987468 Gilmore Many physical systems can exhibit chaotic behavior. Examples include: oscillating chemical systems; lasers driven beyond their threshold of stability; fluids flowing in channels; blood flowing in arteries; neurons sending signals; large coupled electrical systems; etc. Chaotic behavior means briefly that the signals generated by such systems are deterministic (predictable), oscillating, and not periodic. Before we can hope to reach a deep understanding of chaotic behavior, we must be able to classify the different types of chaotic behavior that can exist. Similar problems were faced,and resolved, in the disciplines of Biology (e.g., Linneaus) and Chemistry (e.g., Mendeleef) by scientists who were able to organize a structure for their respective fields. The Principle Investigator has begun the classification scheme for physical systems which can exhibit chaotic behavior by creating a classification scheme for all low dimensional chaotic dynamical systems. He also described in detail how the information necessary to classify such systems can be extracted from experimental data (R. Gilmore, Topological analysis of chaotic dynamical systems, Reviews of Modern Physics 70(4), 1455-1530 (1998)). He will extend this classification scheme to higher dimensional dynamical systems under the current grant.