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Discrete-Time and Discrete-Space Dynamical Systems

  • Kuize Zhang
  • Lijun Zhang
  • Lihua Xie
Book

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 3-33
    3. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 35-56
  3. Boolean Control Networks

    1. Front Matter
      Pages 57-57
    2. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 59-86
    3. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 87-104
    4. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 105-115
    5. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 117-142
  4. Nondeterministic Finite-Transition Systems

    1. Front Matter
      Pages 143-143
    2. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 145-163
    3. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 165-175
  5. Finite-State Automata

    1. Front Matter
      Pages 177-177
    2. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 179-192
  6. Labeled Petri Nets

    1. Front Matter
      Pages 193-193
    2. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 195-209
  7. Cellular Automata

    1. Front Matter
      Pages 211-211
    2. Kuize Zhang, Lijun Zhang, Lihua Xie
      Pages 213-220
  8. Back Matter
    Pages 221-222

About this book

Introduction

Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including:
  • Boolean control networks;
  • nondeterministic finite-transition systems;
  • finite automata;
  • labelled Petri nets; and
  • cellular automata.
The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology.

Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.

Keywords

Boolean Control Network Discrete-time, Discrete-space Dynamical Systems Discrete-event Systems Nondeterministic Finite-Transition Systems Finite Automation Petri Nets Symbolic Dynamics Cellular Automata Semitensor Products Deterministic Boolean networks

Authors and affiliations

  • Kuize Zhang
    • 1
  • Lijun Zhang
    • 2
  • Lihua Xie
    • 3
  1. 1.School of Electrical Engineering and Computer ScienceKTH Royal Institute of TechnologyStockholmSweden
  2. 2.School of Marine Science and TechnologyNorthwestern Polytechnical UniversityXi’anChina
  3. 3.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore

Bibliographic information