Lai Y.-C., Tel T. Transient Chaos: Complex Dynamics on Finite Time Scales

Springer, 2011. - 538 pages.In a dynamical system, transients are temporal evolutions preceding the asymptotic dynamics. Transient dynamics can be more relevant than the asymptotic states of the system in terms of the observation, modeling, prediction, and control of the system. As a result, transients are important to dynamical systems arising from a wide range of disciplines such as physics, chemistry, biology, engineering, economics, and even social sciences. Research on nonlinear dynamical systems has revealed that sustained chaos, as characterized by a random-like yet structured dynamics with sensitive dependence on initial conditions, is ubiquitous in nature. A question is, then, can chaos be transient?A common perception, as conveyed in many existing books on nonlinear dynamics, is that chaos is an asymptotic property that manifests itself only after a long observation. Indeed, standard characteristics of chaos, such as the Lyapunov exponents that measure the exponential separation rates of nearby trajectories and hence quantify the degree of the sensitivity to initial conditions, are defined in the infinite time limit. These features seem to be incompatible with the possibility of chaotic transients.