Bifurcation cascade as chaotic itinerancy with multiple time scales

Abstract

A coupled chaotic system with a variety of time scales is studied. Under a certain condition, it is shown that a change in fast dynamics can influence slow dynamics with a huge time-scale difference, successively through propagation of correlation over elements. This propagation is given by bifurcation cascade, for which three conditions are found to be essential: strong correlation, bifurcation of fast element dynamics by the change of its parameter, and marginal stability. By using coupled Lorenz equation with multiple time scales, it is shown that chaotic itinerancy (CI) observed there leads for the system to satisfy the three conditions, and the bifurcation cascade occurs. Through the analysis of the CI, characteristic properties of the bifurcation cascade, asymmetry in propagation with regards to the time scale, and the universality of the results are discussed, with possible relevance to biological memory.