There has been a renewed interest in the study of nonlinear dynamical systems during the last two decades. This has been partly because of "Chaotic Behavior" which is associated with the study of Dynamical Systems. The research efforts have been devoted to chaos control and chaos synchronization problems in nonlinear science because of its extensive applications. One of the most exciting developments in recent years is the application of dynamical systems techniques to complex networks of interacting components, each having their own internal dynamics, and each being coupled to other nodes. Fluid dynamics is an area that has always had a close relation with chaos. The motion of particles advected by time-dependent flows is a prime example of a chaotic system, and chaotic advection has been observed in many beautiful experiments. Most of the existing theoretical work considers advected particles as having vanishing size, even though it is known that their finite size can have considerable consequences for their dynamics. Hamiltonian dynamics occupies a special place in the area of dynamical systems, because of its applications to classical mechanics, celestial mechanics, physics and other areas. In many Hamiltonian systems, there is a clear separation of slow and fast degrees of freedom, and it is common practice to model the effects of the fast variables by noise and damping, which results in a Langevin equation for the slow degrees of freedom. However, the rigorous mathematical foundations for this are not well-established. One of the biggest current topics of research in the field of dynamical systems is synchronization. Many of the systems in which the concept of synchronization is important are noisy, especially biological systems at the cellular level. It is therefore very important to understand how synchronization works in the presence of noise
The contributions in this book series cover a broad range of interdisciplinary topics between mathematics, circuits, realizations, and practical applications related to nonlinear dynamical systems, nanotechnology, fractals, bifurcation, discrete and continuous chaotic systems, recent techniques for control and synchronization of chaotic systems, computer science, encryption, and information technology.
This book series will include also new circuits and systems based on the new nonlinear elements (memristor, memcapacitor, and meminductor) which have been invented after 2008 and this will help many researchers to solve many nonlinear problems practically. Simply, this book series will achieve the gap between different interdisciplinary applications starting from mathematical concepts, modelling, analysis, and up to the realization and experimental work.
Coverage & Approach
This series emphasizes some mathematical aspects of the theory of dynamical systems. A certain level of mathematical sophistication would be useful throughout the volumes of this series. This series is oriented towards advanced undergraduate or graduate students in mathematics doing applied research. It is also useful to professional researchers in physics, biology, engineering, and economics who use dynamical systems as modeling tools in their studies. Hence a moderate mathematical background in geometry, linear algebra, analysis, differential equations, and dynamical systems is required. Wherever necessary simple mathematical tools are used. The series intends to provide researchers with a solid basis in dynamical systems theory. It would be also useful to researchers in Chaotic Dynamical Systems as it offers a different route to Chaos. Graduate students could profit from it.
Ahmad Taher Azar, PhD, IEEE senior Member, ISA Member
Faculty of Computers and Information, Benha University, Egypt;
School of Engineering and Applied Sciences, Nile University, 6th of October City, Giza, Egypt.
e-mail: firstname.lastname@example.org, email@example.com
Sundarapandian Vaidyanathan, D.Sc.
Professor and Dean, Research and Development Centre, Vel Tech University, Chennai, India