## Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear Systems, Volume 64The intended audience of the book is the group of scientists and engineers who need to deal with nonlinear systems and who are particularly interested in studying the global behavior of these systems. This book introduces such a reader to the methods of cell-to-cell mapping. These methods are believed to provide a new framework of global analysis for nonlinear systems. They are based upon the idea of discretizing a continuum state space into cells, and casting the evolution of a system in the form of a cell-to-cell mapping. Up to now, two kinds of cell-mapping, simple and generalized, have been introduced and studied. These methods allow us to perform the task of locating all the attractors and domains of attraction in an effective manner. Generalized cell-mapping is particularly attractive because it can deal not only with fractally dimensioned entities of deterministic systems, but also with stochastic systems. The main purpose of the book is to make the scattered published results on cell-mapping readily available in one source. The reader, after seeing the power and potential of this new approach, will hopefully want to explore various possibilities of cell-mapping to develop new methodologies for use in his own field of research. |

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1)-multiplet absorption probability acyclic acyclic group affine function algorithm asymptotically stable barycentric coordinates bifurcation boundary cell function cell mapping method cell space cell state space Chapter compute Consider def1ned denoted determined differential equation discussed domains of attraction domiciles dynamical systems eigenvalues expected absorption Figure given global analysis global behavior gradient vectors group number hypersurface image cells in-phase index theory integers iterative L-neighborhood limit cycle limiting probability linear logistic map mapping step Markov chains nondegenerate nonlinear systems number of cells out-of-phase P-1 cell P-K point P-K solution parameter periodic cells periodic solutions persistent cell persistent group point of F probability vector properties regular cells Section shown in Fig simple cell mapping simplex singular cell singular doublet singular entities singular multiplets singular point sink cell strange attractor subgroup Theorem total number trajectories transient cells transient groups transition probability matrix unstable values vector field zero zeroth level