A modified cell-to-cell mapping method for nonlinear systems (Q1802462)

The so-called cell-to-cell mapping method is an approximate method developed by C. S. Hsu and his co-workers to find asymptotically stable equilibria, periodic motions, domains of attraction etc. in nonlinear dynamical systems [a usual reference in this field is the book of \textit{C. S. Hsu}: Cell-to-cell mapping: A method of global analysis for nonlinear systems (1987; Zbl 0632.58002)]. The author proposes a modification of the above method which is concerned with the iterative cell refinement to improve the efficiency of this method, particularly in the case of a system which starts with a fairly coarse structure of state cells. Some applications to the van der Pol and a two compartment enzyme models are presented to show the advantage of the modified over the standard method.