谢勇

Date:

2025-04-30

Title:

Complex Systems: Fractionality, Time-delay and Synchronization (Chapter 6)

Publisher:

高教出版社 & Springer

Brief Introduction:

This edited book covers recent developments on fractional dynamics, time-delay systems, system synchromzation, and neuron dynamics. Fractional calculus is extensively used as a powefful tool to investigate complex phenomena in engineering and science, and has received renewed attention recently. Chapter I of the book investigates fractional dynamics of complex systems. Some recent results and applications in fractional dynamics are presented. In Chapter 2, the synthesis and application of fractional-order controllers are presented. This is an active area of research. The tractional-order PID controllers are designed for the velocity control of an experimental modular servo system. The system consists of a digital servomechanism and open-architecture software environment for real-time implementation. Experimental results of fractional-order controllers are presented and analyzed. The effectiveness and superior perfonnance of the fractional-order controls are compared WIth c1asslcalmteger-order PID controllers. Time delay is a common phenomenon in engineering, economical and biological systems, and has become a popular research topic in recent years. In Chapter 3, equi-librium stability, Lindsedt's method and Hopf bifurcation, and transient behaviors in differential-delay equations are presented. Multiple-scale and the center mani-fold analysis are addressed. These methods are applied to investigate dynamical behaviors of a differential-delay system modeling a section of the DNA molecule. Chapter 4 focuses on the methodologies for time-domain solutions and control de-sign of time-delayed systems. Method of semi-discretization and continuous time approximation are discussed. The spectral properties ofthe methods will be investi-gated. A comparative study of stabIlity of time-delayed linear time invanant systems is carried out by the Lyapunov method, Pad approxImation and semi-discretization. The methods of solution for stochastic dynamical systems with time delay are also discussed, and a number of control examples and an experimental validation are presented. Chapter 5 develops a theory for synchromzation of multiple dynamical systems under constraints The metric functionals based on the constraints are introduced to descnbe the synchronicity of two or more dynamIcal systems. The chapter pro-vides a theoretic framework for designing controllers ofslave systems which can be synchronized with master systems. Finally in Chapter 6, complex dynamics of neurons with time-delay, stochas-ticity and impulsive discontinity are presented. Complex dynamical behaviors include periodic spiking, chaotic spiking, periodic and chaotic bursting, and synchro-nization. In this chapter, a comprehensive review on recent developments and new results in nonlinear neural dynamics are presented. It is our hope that the book presents a reasonably broad view of the state-of-the-art of complex systems, and provides a useful reference volume to scientists, engineers and students. Furthermore, we hope that the book will stimulate more researches in the rapidly evolving and interesting field of complex systems.

Translated or Not:

No

Date of Publication:

2011-01-28

Co-author:

Yong Xie, Jian-Xue Xu