Preface

This issue of Communications on Pure and Applied Analysis, comprises a collection in the general area of nonlinear systems and analysis, and related applications in mathematical biology and engineering. During the past few decades people have seen an enormous growth of the applicability of dynamical systems and the new developments of related dynamical concepts. This has been driven by modern computer power as well as by the discovery of advanced mathematical techniques. Scientists in all disciplines have come to realize the power and beauty of the geometric and qualitative techniques developed during this period. More importantly, they have been able to apply these techniques to a various nonlinear problems ranging from physics and engineering to biology and ecology, from the smallest scales of theoretical particle physics up to the largest scales of cosmic structure. The results have been truly exciting: systems which once seemed completely intractable from an analytical point of view can now be studied geometrically and qualitatively. Chaotic and random behavior of solutions of various systems is now understood to be an inherent feature of many nonlinear systems, and the geometric and numerical methods developed over the past few decades contributed significantly in those areas.