Discontinuity and Complexity in Nonlinear Physical Systems

  • J. A. Tenreiro Machado
  • Dumitru Baleanu
  • Albert C J Luo

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Fractional Dynamics and Nonlinearity

    1. Front Matter
      Pages 1-1
    2. Dumitru Baleanu, Guo-Cheng Wu, Jun-Sheng Duan
      Pages 35-62
    3. Xiao-Jun Yang, Dumitru Baleanu, J. A. Tenreiro Machado
      Pages 63-89
    4. Beyza Billur İskender, Necati Özdemir, Aslan Deniz Karaoglan
      Pages 91-105
    5. 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
    2. R. E. Best, N. V. Kuznetsov, G. A. Leonov, M. V. Yuldashev, R. V. Yuldashev
      Pages 169-192
    3. Françoise Briolle, Xavier Leoncini
      Pages 215-254
  4. Discontinuous Dynamics

    1. Front Matter
      Pages 285-285
    2. M. A. Kiseleva, N. V. Kuznetsov, G. A. Leonov, P. Neittaanmäki
      Pages 287-304

About this book


This unique book 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.

This book also:

·         Provides Lie group analysis with nonlinear self-adjointness 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

Discontinuity and Complexity in Nonlinear Physical Systems is an ideal book for scientific researchers, academics, and graduate students in the field of nonlinear dynamics.


Computational Methods of Engineering Discontinuos Dynamical Systems Engineering Nonlinearity Financial Nonlinearity Fractional Calculus Lie Group Analysis Nonlinearity in Complex Systems

Editors and affiliations

  • J. A. Tenreiro Machado
    • 1
  • Dumitru Baleanu
    • 2
  • Albert C J Luo
    • 3
  1. 1.Department of Electrical EngineeringPolytechnic Institute of Porto Institute of EngineeringPortoPortugal
  2. 2.Faculty of Art and Sciences, Mathematics and Computer SciencesCankaya UniversityAnkaraTurkey
  3. 3.Department of Mechanical EngineeringSouthern Illinois University EdwardsvilleEdwardsvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-01411-1
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-01410-4
  • Online ISBN 978-3-319-01411-1
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • About this book