Chaotic Itinerancy: A Multi-Disciplinary Perspective

Chaotic itinerancy is characterized here as a general mechanism of high-dimensional systems. The paper focuses on the interplay between the low-dimensional behavior in the vicinity of attractors and the transients of the embedding larger system. Using this interplay we chart the relationship of chaotic itinerancy to some other dynamical concepts and applied notions. From the dynamic computational point of view, chaotic itinerancy is shown to extend naturally to the concept of ‘computation with trajectories’, which involves the use of low-dimensional systems based entirely on transients. In a more applied perspective, chaotic itinerancy is discussed in the context of emergent multi-level systems. As an example, molecular dynamics are argued to be conceptualizable in the form of a series of low-dimensional systems which emerge temporarily in a very large system that performs itinerant motion. Finally, as motivated by the properties of chaotic itinerancy, we discuss the phenomenology of high-dimensional systems and its relationship to the problem of universality of dynamics. This is a penultimate draft of a submitted manuscript. Publication details pending, 2003. 02. 05. 2 Chaotic itinerancy has been studied for more than a decade. It was found in a great number of examples which include various natural systems and computer simulations. The principal issue, in most cases, was to understand nonstationary behavior observed in highdimensional systems. Chaotic itinerancy is of more general interest, however. It is used as a theoretical tool in the study of encoding and cryptography, as well as of episodic memory and other biological models of cognition. In this paper the concept of chaotic itinerancy is characterized as a special case for a more general idea, that of computing with trajectories. We discuss both notions from a multi-disciplinary perspective that encompasses biology, chemistry and cognitive science. We draw a picture of chaotic itinerancy as a powerful tool for obtaining dynamical behaviors of a new, important kind of complexity, and we show how the concept of ‘computing with trajectories’ arises naturally in that context. Finally, in a series of remarks about the phenomenology of temporal behavior and the problem of universality of dyamics, we characterize high-dimensional systems from a new viewpoint, partially motivated by the properties of chaotic itinerancy.