Fractal Control and Its Applications

1. Front Matter

   Pages iii-xv

   PDF

2. Introduction

   • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

   Pages 1-2

3. New Characteristics About the Fractal Control Theory

   • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

   Pages 3-36

4. Fractal Control and Synchronization of Classical Model

   • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

   Pages 37-48

5. Control and Synchronization of Julia Sets Generated by a Class of Complex Time-Delay Rational MAP

   • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

   Pages 49-60

6. Control and Synchronization of Spatial Fractals

   • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

   Pages 61-95

7. Fractal Phenomena and Control in Economical Models

   • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

   Pages 97-128

8. Control of Julia Sets in Complex Physical Systems

   • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

   Pages 129-161

9. Applications of Fractal Control in Biologies

   • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

   Pages 163-234

10. Control of the Thermal Fractal Diffusion Systems

    • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

    Pages 235-264

11. Fractal Analysis and Control of the SIRS Models

    • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

    Pages 265-302

12. Application of Fractal Control in Other Fields

    • Shu Tang Liu, Yong Ping Zhang, Chang An Liu

    Pages 303-333

13. Back Matter

    Pages 335-353

    PDF

The book focuses on fractal control and applications in various fields. Fractal phenomena occur in nonlinear models, and since the behaviors depicted by fractals need to be controlled in practical applications, an understanding of fractal control is necessary. This book introduces readers to Julia set fractals and Mandelbrot set fractals in a range of models, such as physical systems, biological systems and SIRS models, and discusses controllers designed to control these fractals. Further, it demonstrates how the fractal dimension can be calculated in order to describe the complexity of various systems.Offering a comprehensive and systematic overview of the practical issues in fractal control, this book is a valuable resource for readers interested in practical solutions in fractal control. It will also appeal to researchers, engineers, and graduate students in fields of fractal control and applications, as well as chaos control and applications.

• fractal control
• synchronization
• Julia set
• Mandelbrot set
• fractal dimension

• College of Control Science and Engineeri, Shandong University, Jinan, China

  Shu Tang Liu

• School of Mathematics and Statistics, Shandong University (Weihai), Weihai, China

  Yong Ping Zhang

• Chinese University of Hong Kong, Hong Kong, China

  Chang An Liu

Shu-Tang Liu, male, professor, tutor of doctoral student, School of control science and engineering, Shandong University. The research areas are theory and applications of fractal control, nonlinear control, chaos and control, bifurcation control theory and applications, physical oceanography, marine ecology and so on. One book has been published by Springer (Shu-Tang Liu and Pei Wang, Fractal control theory, Springer, 2018.5). More than 150 papers have been published in international journals, such as Nonlinear Analysis: Real World Applications, IEEE Trans. Circuits and Systems, Fractal, IEEE Trans. on Nano Bioscience, IEEE Communications Letters, Complexity, Nonlinear Dynamics, International Journal of Bifurcation and Chaos and so on. More than 10 national science projects have been presided including one national key project of natural science foundation of China, one national natural science foundation of China and Shandong joint project, five natural science foundation of China, and two central military commission science and technology commission, national defense science and technology innovation zone military engineering projects, two natural science foundation of Shandong Province. In 2004, he won the national award for 100 excellent doctoral dissertations.

Yong-Ping Zhang, male, professor, tutor of master student, School of mathematics and statistics, Shandong University (Weihai). The research areas are theory and applications of fractal control, nonlinear control, chaos and control and so on. More than 30 papers have been published in international journals, such as Nonlinear Dynamics, Complexity, International Journal of Bifurcation and Chaos, Asian Journal of Control and so on. He has presided one national natural science foundation of China, one natural science foundation of Shandong Province and one China postdoctoral foundation. 


Chang-An Liu, male, postdoctoral research fellow in the Chinese University of Hong Kong. The research areas are Biomedical informatics, biomedical data mining and analysis, computational biomedicine, computational and theoretical neuroscience, Alzheimer’s disease and digestive diseases. Five papers have been published in international journals, such as Frontiers in Aging Neuroscience, Frontiers in Genetics, Journal of Nonlinear Modeling and Analysis and so on.

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