A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

1. Front Matter

   Pages i-viii

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2. From Nonlinear Dynamics to Complex Systems: Introduction

   • Elbert E. N. Macau

   Pages 1-5

3. An Overview of the Generalized Gardner Equation: Symmetry Groups and Conservation Laws

   • M. S. Bruzón, M. L. Gandarias, R. de la Rosa

   Pages 7-26

4. On Symmetries and Conservation Laws for a Generalized Fisher–Kolmogorov–Petrovsky–Piskunov Equation

   • María Luz Gandarias, María de los Santos Bruzón, María Rosa

   Pages 27-50

5. Tunable Orbits Influence in a Driven Stadium-Like Billiard

   • André L. P. Livorati

   Pages 51-67

6. Intermittency and Transport Barriers in Fluids and Plasmas

   • Emanuel V. Chimanski, Caroline G. L. Martins, Roman Chertovskih, Erico L. Rempel, Marisa Roberto, Iberê L. Caldas et al.

   Pages 69-87

7. An Investigation of the Chaotic Transient for a Boundary Crisis in the Fermi-Ulam Model

   • Edson D. Leonel, Murilo F. Marques

   Pages 89-108

8. New Trends in Chaos-Based Communications and Signal Processing

   • Marcio Eisencraft, João V. C. Evangelista, Rafael A. Costa, Rodrigo T. Fontes, Renato Candido, Daniel P. B. Chaves et al.

   Pages 109-129

9. Modeling Fireflies Synchronization

   • Gonzalo Marcelo Ramírez-Ávila, Jürgen Kurths, Stéphanie Depickère, Jean-Louis Deneubourg

   Pages 131-156

10. From Flocs to Flocks

    • Shannon Dee Algar, Thomas Stemler, Michael Small

    Pages 157-175

11. Network Centrality: An Introduction

    • Francisco Aparecido Rodrigues

    Pages 177-196

12. Characterizing Flows by Complex Network Methods

    • Reik V. Donner, Michael Lindner, Liubov Tupikina, Nora Molkenthin

    Pages 197-226

13. Back Matter

    Pages 227-228

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This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls.

·         Introduces new concepts for understanding and modeling complex systems;

·         Explains risk reduction management in complex systems;

·         Examines the symmetry group approach tounderstanding complex systems;

·         Illustrates the relation between transient chaos and crises.

• Nonlinear differential systems
• Chaos and complexity
• Chaotic systems
• Complex systems
• Risk management in complex systems
• Nonlinear systems
• Transient chaos
• Barriers in Hamiltonian systems
• Symmetry group
• Nonlinear signal processing
• Synchronization
• complexity

• Instituto Nacional de Pesquisas Espaciais – INPE, São José dos Campos, Brazil

  Elbert E. N. Macau

Dr. Elbert E. N. Macau is a Professor within the Laboratory for Applied Mathematics and Computing (LAC), National Institute for Space Research, Sao Jose dos Campos, Brazil. He is an internationally recognized researcher with expertise in Nonlinear Dynamics, Dynamics, Nonlinear Systems, Mathematical Modelling, Chaos Theory, and Applied Mathematics.

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