Combinatorial Optimization

The behavior of nonlinear dynamical systems can differ completely from that of linear dynamical systems. Regular oscillatory motion as well as seemingly irregular motion can emerge in these systems without resort to exogenous influences or peculiar parameter values. Recent mathematical advances made in the theory of nonlinear dynamical systems allow the restrictive linear approach to dynamical phenomena in economics to be discarded and observable fluctuations of economic variables to be modelled in a simple and convenient way. This book attempts to familiarize the reader with the standard tools in nonlinear dynamical systems theory. The usage of these tools is demonstrated with simple examples from different fields like business cycle theory, optimal control theory, growth theory, and population dynamics. The presentation encompasses a short reminder of linear dynamical systems and traditional themes in nonlinear systems like the existence and uniqueness of limit cycles and closed orbits in predator-prey systems. The main part of the book deals with chaotic motion in economic systems. It is demonstrated, that irregular dynamical behavior can be generated in deterministic economic systems with relative ease, once the linear approach in modelling dynamic phenomena is abandoned. One-dimensional and higher-dimensional difference equations as well as higher-dimensional differential equation systems are discussed and illustrated with a variety of economic examples. Recently emerging techniques for discriminating stochastic and deterministic dynamical systems are presented, as well as the question of whether the nature of actual economic time series is chaotic or stochastic.Simeone, B. is the author of 'Combinatorial Optimization', published 2008 under ISBN 9783540517979 and ISBN 3540517979.