Authoritative and visionary, this festschrift features 12 highly readable expositions of virtually all currently active aspects of nonlinear science. It has been painstakingly researched and written by leading scientists and eminent expositors, including L Shilnikov, R Seydel, I Prigogine, W Porod, C Mira, M Lakshmanan, W Lauterborn, A Holden, H Haken, C Grebogi, E Doedel and L Chua; each chapter addresses a current and intensively researched area of nonlinear science and chaos, including nonlinear dynamics, mathematics, numerics and technology. Handsomely produced with high resolution color graphics for enhanced readability, this book has been carefully written at a high level of exposition and is somewhat self-contained. Each chapter includes a tutorial and background information, as well as a survey of each area's main results and state of the art. Of special interest to both beginners and seasoned researchers is the identification of future trends and challenging yet tractable problems thatare likely,to be solved before the end of the 21st century. The visionary and provocative nature of this book makes it a valuable and lasting reference.

Revolutionary and original, this treatise presents a new paradigm of Emergence and Complexity, with applications drawn from numerous disciplines, including artificial life, biology, chemistry, computation, physics, image processing, information science, etc. CNN is an acronym for Cellular Neural Networks when used in the context of brain science, or Cellular Nonlinear Networks, when used in the context of emergence and complexity. A CNN is modeled by cells and interactions: cells are defined as dynamical systems and interactions are defined via coupling laws. The CNN paradigm is a universal Turing machine and includes cellular automata and lattice dynamical systems as special cases. While the CNN paradigm is an example of Reductionism par excellence, the true origin of emergence and complexity is traced to a much deeper new concept called local activity. The numerous complex phenomena unified under this mathematically precise principle include self organization, dissipative structures, synergetics, order from disorder, far-from-thermodynamic equilibrium, collective behaviors, edge of chaos, etc. Written with a high level of exposition, this completely self-contained monograph is profusely illustrated with over 200 stunning color illustrations of emergent phenomena.

In this book, the reader will find a theoretical introduction to noninteger order systems, as well as several applications showing their features and peculiarities. The main definitions and results of research on noninteger order systems and modelling of physical noninteger phenomena are reported together with problems of their approximation. Control applications, noninteger order CNNs and circuit realizations of noninteger order systems are also presented.The book is intended for students and researchers involved in the simulation and control of nonlinear noninteger order systems, with particular attention to those involved in the study of chaotic systems and the modelling of nonlinear spatiotemporal phenomena.

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Cellular Neural Networks (CNNs) constitute a class of nonlinear, recurrent and locally coupled arrays of identical dynamical cells that operate in parallel. ANALOG chips are being developed for use in applications where sophisticated signal processing at low power consumption is required. Signal processing via CNNs only becomes efficient if the network is implemented in analog hardware. In view of the physical limitations that analog implementations entail, robust operation of a CNN chip with respect to parameter variations has to be insured. By far not all mathematically possible CNN tasks can be carried out reliably on an analog chip; some of them are inherently too sensitive. This book defines a robustness measure to quantify the degree of robustness and proposes an exact and direct analytical design method for the synthesis of optimally robust network parameters. The method is based on a design centering technique which is generally applicable where linear constraints have to be satisfied in an optimum way. Processing speed is always crucial when discussing signal-processing devices. In the case of the CNN, it is shown that the setting time can be specified in closed analytical expressions, which permits, on the one hand, parameter optimization with respect to speed and, on the other hand, efficient numerical integration of CNNs. Interdependence between robustness and speed issues are also addressed. Another goal pursued is the unification of the theory of continuous-time and discrete-time systems. By means of a delta-operator approach, it is proven that the same network parameters can be used for both of these classes, even if their nonlinear output functions differ. More complex CNN optimization problems that cannot be solved analytically necessitate resorting to numerical methods. Among these, stochastic optimization techniques such as genetic algorithms prove their usefulness, for example in image classification problems. Since the inception of the CNN, the problem of finding the network parameters for a desired task has been regarded as a learning or training problem, and computationally expensive methods derived from standard neural networks have been applied. Furthermore, numerous useful parameter sets have been derived by intuition. In this book, a direct and exact analytical design method for the network parameters is presented. The approach yields solutions which are optimum with respect to robustness, an aspect which is crucial for successful implementation of the analog CNN hardware that has often been neglected. `This beautifully rounded work provides many interesting and useful results, for both CNN theorists and circuit designers.' Leon O. Chua

This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time ? two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler.

This new edition also treats smart materials and artificial life. A new chapter on information and computational dynamics takes up many recent discussions in the community.