© 2011

Fractional-Order Nonlinear Systems

Modeling, Analysis and Simulation


  • Clearly presents the stability theory of fractional dynamical systems, with examples

  • Easy to understand the complex concepts in fractional dynamical systems

  • Integrates Matlab programs and Simulink models for interactive learning


Part of the Nonlinear Physical Science book series (NPS)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Ivo Petráš
    Pages 1-5
  3. Ivo Petráš
    Pages 7-42
  4. Ivo Petráš
    Pages 43-54
  5. Ivo Petráš
    Pages 55-101
  6. Ivo Petráš
    Pages 103-184
  7. Ivo Petráš
    Pages 185-199
  8. Ivo Petráš
    Pages 201-205
  9. Back Matter
    Pages 207-218

About this book


"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order.

The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level.  

Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.


Control of chaos Fractional calculus Fractional chaotic systems HEP Matlab programs chaos NPS Simulink models Stability of fractional order systems

Authors and affiliations

  1. 1.Technical University of Košice, Faculty of BERGKošiceSlovak Republic

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From the reviews:

“The principal goal of this monograph is to introduce the reader to a new and rapidly growing branch of dynamical systems called fractional-order chaotic systems. … the book is a very nice first step towards a systematic description of this new and interesting direction of research. The monograph can be used by graduate students and researchers working with chaotic dynamical systems, control, synchronization and related fields.” (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1228, 2012)