Nonlinear Perron Frobenius Theory
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Nonlinear Perron-Frobenius Theory
In the past several decades the classical Perron-Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron-Frobenius theory has found significant uses in computer science, mathematical biology, game theory and the study of dynamical systems. This is the first comprehensive and unified introduction to nonlinear Perron-Frobenius theory suitable for graduate students and researchers entering the field for the first time. It acquaints the reader with recent developments and provides a guide to challenging open problems. To enhance accessibility, the focus is on finite dimensional nonlinear Perron-Frobenius theory, but pointers are provided to infinite dimensional results. Prerequisites are little more than basic real analysis and topology.
Nonlinear Perron-Frobenius Theory
Author: Bas Lemmens
language: en
Publisher: Cambridge University Press
Release Date: 2012-05-03
Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.
Positive Dynamical Systems in Discrete Time
Author: Ulrich Krause
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2015-11-27
This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a system are nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds application in electrical engineering, physics and computer sciences. "The author has greatly expanded the field of positive systems in surprising ways." - Prof. Dr. David G. Luenberger, Stanford University(USA)