Nonlinear Systems, Vol. 1, Softcover reprint of the original 1st ed. 2018 Mathematical Theory and Computational Methods Understanding Complex Systems Series

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.

Part 1 - Bifurcation Analysis.- Analytic integrability of some degenerate centers.- Analysis of the Hopf-zero bifurcation and their degenerations in a quasi-Lorenz system.- Normal forms for a class of tridimensional vector fields with free-divergence in its first component.- Takens-Bogdanov bifurcations and resonances of periodic orbits in the Lorenz system.- Part 2 - Wave Equations.- Solitons and vortices in the Nonlinear Dirac Equation.- Stochastic Korteweg - de Vries type equations.- Exact and adiabtic invariants of KdV type equations.- Gravitational waves as nonlinear waves and solitons.- Part 3 - Other Differential and Difference Equations.- On the dynamics of the nonlinear logistic difference equation with two delays.- Simplifying singular perturbation theory in the canard regime using piecewise-linear (PWL) systems.- Principal solutions and variation of constants formula for a class of functional differential equations.- Diffusion Equations in Inhomogeneous Media from the Master Equation.- Part 4 - Computational Methods.- On the numerical approximation to generalized Ostrovsky equations.- Simulation of Laser Dynamics with Cellular Automata: progress and challenges.

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-linea

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).

His research covers many aspects of Nonlinear Science and is based inthe the