Regularity and Stochasticity of Nonlinear Dynamical Systems

  • Dimitri Volchenkov
  • Xavier Leoncini

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 21)

Table of contents

  1. Front Matter
    Pages i-x
  2. Vadim Anishchenko, Nadezhda Semenova, Elena Rybalova, Galina Strelkova
    Pages 19-49
  3. M. U. Akhmet, A. Kıvılcım
    Pages 111-159
  4. Alexander N. Pisarchik, Mariano Alberto García-Vellisca
    Pages 181-198
  5. P. Domínguez, M. A. Montes de Oca, G. J. F. Sienra
    Pages 199-218
  6. Vladimir Klinshov, Dmitry Shchapin, Serhiy Yanchuk, Vladimir Nekorkin
    Pages 219-246
  7. Back Matter
    Pages 309-311

About this book


This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

  • Presents the most up-to-date understanding in nonlinear dynamical systems along with new theories and methodologies applied to nonlinear physics, engineering, and social science;
  • Includes differential-invariant solutions, classification of orientable horseshoes, and nonlinear time-delay systems;
  • Illustrates solution routes to chaos for nonlinear differential equations.


Nonlinear differential equation solvability Differential-invariant solutions Classification of orientable horseshoes From periodic motions to chaos From chaos to order Nonlinear time-delay systems Grazing in Impulsive differential equations Nonlinear time-delay systems Impulsive dynamical systems Uncertainty in success, hierarchy and inequality

Editors and affiliations

  • Dimitri Volchenkov
    • 1
  • Xavier Leoncini
    • 2
  1. 1.Department of Mathematics and StatisticsTexas Tech UniversityLubbockUSA
  2. 2.Centre de Physique ThéoriqueAix-Marseille UniversitéMarseilleFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-58061-6
  • Online ISBN 978-3-319-58062-3
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • Buy this book on publisher's site