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Positive Dynamical Systems in Discrete Time: Theory, Models, and Applications

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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 systemare 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.

Abstract:
A dynamical system is positive when all relevant variables of a systemare nonnegative in a natural way. This book provides a systematic, rigorous and self-contained treatment of positive dynamical  Read more...

Author(s): Krause, Ulrich
Series: Gruyter series in mathematics and life sciences 5
Publisher: de Gruyter
Year: 2015

Language: English
Pages: 366
City: Berlin/Boston
Tags: Lo

Content: Frontmatter --
Preface --
Contents --
Notation --
List of Figures --
1. How positive discrete dynamical systems do arise --
2. Concave Perron-Frobenius theory --
3. Internal metrics on convex cones --
4. Contractive dynamics on metric spaces --
5. Ascending dynamics in convex cones of infinite dimension --
6. Limit set trichotomy --
7. Non-autonomous positive systems --
8. Dynamics of interaction: opinions, mean maps, multi-agent coordination, and swarms --
Index --
Backmatter.