Fractal Control and Its Applications

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.

Introduction.- New Characteristics about the Fractal Control Theory.- Fractal Control and Synchronization of Classical Model.- Control and Synchronization of Julia Sets Generated by a Class of Complex Time-Delay Rational MAP.- Control and Synchronization of Spatial Fractals.- Fractal Phenomena and Control in Economical Models.- Control of Julia Sets in Complex Physical Systems.- Applications of Fractal Control in Biologies.- Control of the Thermal Fractal Diffusion Systems.- Fractal Analysis and Control of the SIRS Models.- Application of Fractal Control in Other Fields.- References

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.