title: Defining chaos.
abstract: In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.
authors.affiliation: Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Brian R
authors.initials: BR
authors.lastname: Hunt
authors.affiliation: Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Edward
authors.initials: E
authors.lastname: Ott