Phase-Locked Loops (PLLs) are electronic systems that can be used as a synchronized oscillator, a driver or multiplier of frequency, a modulator or demodulator and as an amplifier of phase modulated signals. This book describes the methods used in the analysis of PLLs.

Discusses the applications of chaos control methods in circuits and systems. This book emphasises on bridging the gap between chaos control methods and circuits and systems.

A gallery of nearly 900 "chaotic attractors" ???????????? some generated by Chua's physical circuit, the majority through computer simulation of the circuit and its generalizations ???????????? are illustrated as 3D color images, time series and fast Fourier transform algorithms. For interested researchers, also presented is the information necessary to replicate the behaviors and images. Finally, how the

Focuses on the research topics investigated during the three-year research project funded by the Italian Ministero dell'Istruzione, dell'Universita e della Ricerca under the FIRB project RBNE01CW3M. This book presents the final results of the project after a general introduction to the subject.

This book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology and communication or laser physics. Over the last decade, a number of new types of synchronization have been identified and some interesting new ideas concerning the synchronization have also appeared.

This book presents the complete synchronization problem rather than just results from the research. The problem is demonstrated in relation...

Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli σ_τ-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and...

Presents a fresh approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems.

This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are nonlinear oscillations, deterministic chaos, solitons, reactiondiffusion-driven chemical pattern formation, neuron dynamics, autocatalysis and molecular evolution. Included is a discussion of processes from the vantage of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from...

This unprecedented book offers all the details of the mathematical mechanics underlying modern modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding. The method is to take advantage of latest mathematical technologies -- Eilenberg-Mac Lane category theory, Robinson infinitesimal calculus and Kolmogorov probability theory -- to explicate Particle Mechanics, The Theory of Substances (categorical thermodynamics), and computer simulation using a diagram-based parallel programming language...

This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the H non map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters. Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two...