Some advances on global analysis of nonlinear systems

Global analysis in nonlinear dynamics means the study of attractors and their basins of attraction; meanwhile a lot of complex dynamical behaviors and new phenomena are concerned such as fractal basin boundary, Wada basin boundary, infinite unstable periodic orbits embedded in chaotic attractor, chaotic saddle and transient chaos, crises, riddled basin of attractor, stochastic global dynamics, etc. To analyze the global dynamics analytically is difficult and interesting while the results are few. Then, the numerical analysis for global dynamics is usually the main approach. Global analysis captures both the interest and imagination of the wider communities in various fields, such as mathematics, physics, meteorology, life science, computational science, engineering, medicine, and others. Emphasis is put mainly on the development in this global dynamics field in China. (C) 2009 Published by Elsevier Ltd.