AN ITERATIVE METHOD OF POINT MAPPING UNDER CELL REFERENCE FOR THE GLOBAL ANALYSIS OF NONLINEAR DYNAMICAL-SYSTEMS

An iterative method of point mapping under cell reference for the glob al analysis of non-linear dynamical systems is proposed. To build a ce ll reference, a cell co-ordinate system, in additional to the original Cartesian system, is first established in the state space to construc t a cell space, and then characteristic functions are defined in the c ell space. With the cell reference, the global characteristic informat ion of a dynamical system involved in generating trajectories in the E uclidian state space can be effectively captured and used to determine the characters of cells, or the collective dynamical characteristics of the points in sub-regions of the state space. After the characters of some cells are determined, these character confirmed cells can be u sed to determine the characters of the trajectories in the Euclidian s tate space. To facilitate the implementation, the present method consi sts of an initial procedure and an iterative procedure. As shown by ap plications, the present method can effectively share the advantages of the previous global analysis methods but also eliminate their weaknes ses. (C) 1996 Academic Press Limited