Nonlinear Systems, Vol. 1

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 r systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49: 609 (2002).

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.