Book Description
Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.
Author : Bas Lemmens
Publisher : Cambridge University Press
Page : 337 pages
File Size : 38,17 MB
Release : 2012-05-03
Category : Mathematics
ISBN : 0521898811
Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.
Author : Bas Lemmens
Publisher :
Page : 323 pages
File Size : 28,45 MB
Release : 2012
Category : Algebras, Linear
ISBN : 9781107226340
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.
Author : Ulrich Krause
Publisher : Walter de Gruyter GmbH & Co KG
Page : 366 pages
File Size : 24,68 MB
Release : 2015-03-10
Category : Mathematics
ISBN : 3110365693
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)
Author : A. Neumaier
Publisher : Cambridge University Press
Page : 275 pages
File Size : 12,6 MB
Release : 1990
Category : Mathematics
ISBN : 052133196X
Mathematics of Computing -- Numerical Analysis.
Author : Ulrich Krause
Publisher : Walter de Gruyter GmbH & Co KG
Page : 429 pages
File Size : 36,67 MB
Release : 2015-11-27
Category : Mathematics
ISBN : 3110391341
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)
Author : Viviane Baladi
Publisher : World Scientific
Page : 332 pages
File Size : 10,70 MB
Release : 2000
Category : Science
ISBN : 9789810233280
Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system ?mixes?, i.e. ?forgets? its initial conditions.This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained.The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum.
Author : Yury Kochetov
Publisher : Springer Nature
Page : 358 pages
File Size : 20,10 MB
Release : 2022-09-29
Category : Mathematics
ISBN : 3031162242
This book constitutes refereed proceedings of the 21st International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2022, held in Petrozavodsk, Russia, in July 2022. The 21 full papers and 3 short papers presented in this volume were carefully reviewed and selected from a total of 88 submissions. The papers in the volume are organised according to the following topical headings: invited talks; integer programming and combinatorial optimization; mathematical programming; game theory and optimal control; operational research applications.
Author : K. Kaneko
Publisher :
Page : 208 pages
File Size : 35,16 MB
Release : 1993-04-13
Category : Mathematics
ISBN :
The technique of the coupled map lattice (CML) is a rapidly developing field in nonlinear dynamics at present. This book gives a fully illustrative overview of current research in the field. A CML is a dynamical system in which there is some interaction ('coupled') between continuous state elements, which evolve in discrete time ('map') and are distributed on a discrete space ('lattice'). This book investigates both the theoretical aspects and applications of CMLs to spatially extended systems in nonlinear dynamical systems.
Author : Alexandre Mauroy
Publisher : Springer Nature
Page : 568 pages
File Size : 23,73 MB
Release : 2020-02-22
Category : Technology & Engineering
ISBN : 3030357139
This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory. The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts: theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification; data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; and Koopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control. A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.
Author : Benjamin Dodson
Publisher : Cambridge University Press
Page : 255 pages
File Size : 45,19 MB
Release : 2019-03-28
Category : Mathematics
ISBN : 1108472087
Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and energy-critical Schrödinger equations.