Global Analysis of Nonlinear Dynamical Systems

This chapter discusses recent applications and algorithm developments of the cell mapping methods, which were created by C. S. Hsu in 1980s for global analysis of nonlinear dynamical systems. Such systems can have multiple steady-state responses including equilibrium states, periodic motions, chaotic attractors as well as domains of attraction of these steady-state responses. Without the cell mapping methods, these dynamical responses would have been far more difficult to obtain. Since the creation of them, the cell mapping methods have enjoyed attention from the research communities. New extensions of the methods and new algorithms including parallel computing have been developed in the past few decades. The cell mapping methods have also been applied to global analysis and control design of deterministic, stochastic and fuzzy dynamical systems. Representative examples of new applications are presented in this chapter.