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Discontinuity and Complexity in Nonlinear Physical Systems

  • Book
  • © 2014

Overview

Editors:
  1. J. A. Tenreiro Machado

    1. Department of Electrical Engineering, Polytechnic Institute of Porto Institute of Engineering, Porto, Portugal

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  2. Dumitru Baleanu

    1. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

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  3. Albert C J Luo

    1. Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, USA

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  • Provides Lie group analysis with nonlinear self-adjointess and conservation laws
  • Presents computational methods and control in fractional calculus
  • Discusses discontinuous dynamics and chaos in drilling systems and vibro-impact systems
  • Illustrates the mechanism and dynamics of shock waves and dynamical stability
  • Includes supplementary material: sn.pub/extras

Part of the book series: Nonlinear Systems and Complexity (NSCH, volume 6)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Fractional Dynamics and Nonlinearity

    1. Front Matter

      Pages 1-1
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    2. Nonlinear Self-Adjointness for some Generalized KdV Equations

      • M. L. Gandarias, M. Rosa
      Pages 3-21

    3. Weak Self-Adjointness and Conservation Laws for a Family of Benjamin-Bona-Mahony-Burgers Equations

      • M. S. Bruzón
      Pages 23-34

    4. Some Analytical Techniques in Fractional Calculus: Realities and Challenges

      • Dumitru Baleanu, Guo-Cheng Wu, Jun-Sheng Duan
      Pages 35-62

    5. Application of the Local Fractional Fourier Series to Fractal Signals

      • Xiao-Jun Yang, Dumitru Baleanu, J. A. Tenreiro Machado
      Pages 63-89

    6. Parameter Optimization of Fractional Order PI λ D μ Controller Using Response Surface Methodology

      • Beyza Billur Ä°skender, Necati Özdemir, Aslan Deniz Karaoglan
      Pages 91-105

    7. Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative

      • Arkadiusz Syta, Grzegorz Litak
      Pages 107-112

    8. Fractional Calculus: From Simple Control Solutions to Complex Implementation Issues

      • Cristina I. Muresan
      Pages 113-134

    9. Emerging Tools for Quantifying Unconscious Analgesia: Fractional-Order Impedance Models

      • Amélie Chevalier, Dana Copot, Clara M. Ionescu, J. A. Tenreiro Machado, Robin De Keyser
      Pages 135-149

  3. Chaos and Complexity

    1. Front Matter

      Pages 151-151
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    2. 1D Cahn–Hilliard Dynamics: Coarsening and Interrupted Coarsening

      • Simon Villain-Guillot
      Pages 153-168

    3. Nonlinear Analysis of Phase-locked Loop-Based Circuits

      • R. E. Best, N. V. Kuznetsov, G. A. Leonov, M. V. Yuldashev, R. V. Yuldashev
      Pages 169-192

    4. Approaches to Defining and Measuring Assembly Supply Chain Complexity

      • V. Modrak, D. Marton
      Pages 193-213

    5. Non-commutative Tomography: Applications to Data Analysis

      • Françoise Briolle, Xavier Leoncini
      Pages 215-254

    6. Projective Synchronization of Two Gyroscope Systems with Different Motions

      • Fuhong Min, Albert C. J. Luo
      Pages 255-272

    7. Measuring and Analysing Nonlinearities in the Lung Tissue

      • Clara M. Ionescu
      Pages 273-283

  4. Discontinuous Dynamics

    1. Front Matter

      Pages 285-285
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    2. Drilling Systems: Stability and Hidden Oscillations

      • M. A. Kiseleva, N. V. Kuznetsov, G. A. Leonov, P. Neittaanmäki
      Pages 287-304

    3. Chaos in a Piecewise Linear System with Periodic Oscillations

      • Chunqing Lu
      Pages 305-313
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Keywords

About this book

Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis.  Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed.

Editors and Affiliations

  • Department of Electrical Engineering, Polytechnic Institute of Porto Institute of Engineering, Porto, Portugal

    J. A. Tenreiro Machado

  • Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  • Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, USA

    Albert C J Luo

About the editors

José António Tenreiro Machado is Professor, Institute of Engineering, Polytechnic of Porto, Portugal; Dumitru Baleanu is Professor, Department of Mathematics and Computer SciencesCankaya University, Turkey;  Albert Luo is Professor of Mechanical ngineering, Southern Illinois University/Edwardsville, USA

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