Springer Nonlinear Systems, Vol. 1: Mathematical Theory and Computational Methods (Understanding Complex Systems)

This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics. From the Back Cover This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics. About the Author Prof. Victoriano Carmona Centeno obtained his PhD in Mathematics in 2002 at the University of Seville, Spain, under the supervision of Prof. E. Freire and Prof. F. Torres. His PhD Thesis was awarded with the Extraordinary Prize of Town Hall of Sevilla. Currently, he is an Associate Professor at the Department of Applied Mathematics II of the University of Seville. His research covers different aspects of Dynamical Systems, in particular, those related to piecewise smooth systems of differential equations. He is an active member of the Group of Dynamical Systems in Engineering of the University of Sevilla.  Prof. Victoriano Carmona is author of many scientific publications in international journals, books and conferences proceedings. Some of these works have been highly cited and they are basic references in the field of piecewise linear dynamical systems. For instance, V. Carmona, E. Freire and F. Torres, On simplifying and classifying piecewise-linear systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49: 609 (2002). He has reviewed many papers in international journals (for instance, Physica D, Nonlinearity, Proceedings London Mathematical Society,…). He has taken part in the organization of several international conferences, the most recent one in Sevilla (Spain, 2016). Prof. Jesús Cuevas-Maraver obtained his PhD in Physics in 2003 in the Department of Condensed Matter Physics of the University of Seville, Spain, under the supervision of Prof. Francisco R. Romero and Prof. Juan F.R. Archilla.  Presently he is as Associate Professor at the Department of Applied Physics I of the same university. His lectures in Elementary Physics (Mechanics, Thermodynamics and Electromagnetism) take place at the Polytechnic School in the degree of Industrial Chemical Engineering.   His research covers many aspects of Nonlinear Science and is based in the theoretical study of nonlinear localized waves as solitons, kinks or breathers that emerge in many physics systems. He has considered a wide range of such systems, which includes crystals, biomolecules, Bose-Einstein condensates, waveguide arrays, nonlinear circuits or transmission lines and metamaterials. He is a frequent referee in international journals, including Nature Physics, Physical Review Letters or Optics Letters.  Prof. Jesús Cuevas-Maraver has written 96 scientific publications covering international journals and books. He has been author of several chapters in Springer books (P.G. Kevrekidis (ed.), The Discrete Non