This fourth edition of Stochastic Methods is thoroughly revised and augmented, and has been completely reset. While keeping to the spirit of the book I wrote originally, I have reorganised the chapters of Fokker-Planck equations and those on appr- imation methods, and introduced new material on the white noise limit of driven stochastic systems, and on applications and validity of simulation methods based on the Poisson representation. Further, in response to the revolution in ?nancial m- kets following from the discovery by Fischer Black and Myron Scholes of a reliable option pricing...
This fourth edition of Stochastic Methods is thoroughly revised and augmented, and has been completely reset. While keeping to the spirit of the book ...
The widespread interest this book has found among professors, scientists and stu- dents working in a variety of fields has made a new edition necessary. I have used this opportunity to add three new chapters on recent developments. One of the most fascinating fields of modern science is cognitive science which has become a meet- ing place of many disciplines ranging from mathematics over physics and computer science to psychology. Here, one of the important links between these fields is the concept of information which, however, appears in various disguises, be it as Shan- non information or...
The widespread interest this book has found among professors, scientists and stu- dents working in a variety of fields has made a new edition necessar...
This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in...
This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on sys...
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal...
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interfa...
This book addresses a subject at the crossing point of two lines of investi- gation - synergetics and modern nonlinear optics. First, the book is devoted to optical patterns that previously were mainly attributed to the display of instabilities of homogeneous field distributions. Second, we deal with optical bistability and hysteresis, which historically were studied predominantly for point (lumped, spatially nondistributed) systems. In the book, which seems to be the first monograph devoted to opti- cal patterns, I attempt to demonstrate that the variety of optical patterns and other...
This book addresses a subject at the crossing point of two lines of investi- gation - synergetics and modern nonlinear optics. First, the book is devo...
The vulnerability of our civilization to earthquakes is rapidly growing, rais- ing earthquakes to the ranks of major threats faced by humankind. Earth- quake prediction is necessary to reduce that threat by undertaking disaster- preparedness measures. This is one of the critically urgent problems whose solution requires fundamental research. At the same time, prediction is a ma- jor tool of basic science, a source of heuristic constraints and the final test of theories. This volume summarizes the state-of-the-art in earthquake prediction. Its following aspects are considered: - Existing...
The vulnerability of our civilization to earthquakes is rapidly growing, rais- ing earthquakes to the ranks of major threats faced by humankind. Earth...
This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or even the heart muscle, to name but a few. The book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.
This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as elec...
Brain Dynamics serves to introduce graduate students and nonspecialists from various backgrounds to the field of mathematical and computational neurosciences. Some of the advanced chapters will also be of interest to the specialists. The book approaches the subject through pulse-coupled neural networks, with at their core the lighthouse and integrate-and-fire models, which allow for the highly flexible modelling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. Topics also include pulse-averaged equations and their application to...
Brain Dynamics serves to introduce graduate students and nonspecialists from various backgrounds to the field of mathematical and ...
Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Ito calculus applied to the...
Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturb...
Cities first came into existence more than five thousand years ago. How to deal with these partly fascinating, partly frightening creatures of mankind, both practically and intellectually, concerns all of us and, in particular, presents areal challenge to city planners. Each historical epoch has had its own par- ticular attitudes associated with the "Zeitgeist." Accordingly, the planning and steering of cities were based on quite different criteria. But in spite of these differences, the concept of planning and steering was, and still is, the cornerstone of our dealing with cities....
Cities first came into existence more than five thousand years ago. How to deal with these partly fascinating, partly frightening creatures of mankind...
