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Author: Nils Berglund
Publisher: Springer Science & Business Media
Published: 2006-02-07
Total Pages: 283
ISBN-13: 1846281865
DOWNLOAD EBOOKStochastic Differential Equations have become increasingly important in modelling complex systems in physics, chemistry, biology, climatology and other fields. This book examines and provides systems for practitioners to use, and provides a number of case studies to show how they can work in practice.
Author: Michael Grinfeld
Publisher: John Wiley & Sons
Published: 2015-01-12
Total Pages: 634
ISBN-13: 3527411887
DOWNLOAD EBOOKThe new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.
Author: Wolfgang Siegert
Publisher: Springer Science & Business Media
Published: 2009
Total Pages: 264
ISBN-13: 3540859632
DOWNLOAD EBOOKEstablishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
Author: Jürgen Jost
Publisher: Springer Science & Business Media
Published: 2014-02-13
Total Pages: 233
ISBN-13: 1447163532
DOWNLOAD EBOOKMathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for the emerging field of systems biology. Mathematical Methods in Biology and Neurobiology introduces and develops these mathematical structures and methods in a systematic manner. It studies: • discrete structures and graph theory • stochastic processes • dynamical systems and partial differential equations • optimization and the calculus of variations. The biological applications range from molecular to evolutionary and ecological levels, for example: • cellular reaction kinetics and gene regulation • biological pattern formation and chemotaxis • the biophysics and dynamics of neurons • the coding of information in neuronal systems • phylogenetic tree reconstruction • branching processes and population genetics • optimal resource allocation • sexual recombination • the interaction of species. Written by one of the most experienced and successful authors of advanced mathematical textbooks, this book stands apart for the wide range of mathematical tools that are featured. It will be useful for graduate students and researchers in mathematics and physics that want a comprehensive overview and a working knowledge of the mathematical tools that can be applied in biology. It will also be useful for biologists with some mathematical background that want to learn more about the mathematical methods available to deal with biological structures and data.
Author: Jan Awrejcewicz
Publisher: BoD – Books on Demand
Published: 2017-11-29
Total Pages: 256
ISBN-13: 953513633X
DOWNLOAD EBOOKResonance is a common phenomenon, which is observed both in nature and in numerous devices and structures. It occurs in literally all types of vibrations. To mention just a few examples, acoustic, mechanical, or electromagnetic resonance can be distinguished. In the present book, 12 chapters dealing with different aspects of resonance phenomena have been presented.
Author: Leszek Gawarecki
Publisher: Springer Science & Business Media
Published: 2010-11-29
Total Pages: 300
ISBN-13: 3642161944
DOWNLOAD EBOOKThe systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.
Author: Bernhelm Booss
Publisher: Springer Nature
Published: 2024
Total Pages: 514
ISBN-13: 3031451058
DOWNLOAD EBOOKZusammenfassung: This highly interdisciplinary volume brings together a carefully curated set of case studies examining complex systems with multiple time scales (MTS) across a variety of fields: materials science, epidemiology, cell physiology, mathematics, climatology, energy transition planning, ecology, economics, sociology, history, and cultural studies. The book addresses the vast diversity of interacting processes underlying the behaviour of different complex systems, highlighting the multiplicity of characteristic time scales that are a common feature of many and showcases a rich variety of methodologies across disciplinary boundaries. Self-organizing, out-of-equilibrium, ever-evolving systems are ubiquitous in the natural and social world. Examples include the climate, ecosystems, living cells, epidemics, the human brain, and many socio-economic systems across history. Their dynamical behaviour poses great challenges in the pressing context of the climate crisis, since they may involve nonlinearities, feedback loops, and the emergence of spatial-temporal patterns, portrayed by resilience or instability, plasticity or rigidity; bifurcations, thresholds and tipping points; burst-in excitation or slow relaxation, and worlds of other asymptotic behaviour, hysteresis, and resistance to change. Chapters can be read individually by the reader with special interest in such behaviours of particular complex systems or in specific disciplinary perspectives. Read together, however, the case studies, opinion pieces, and meta-studies on MTS systems presented and analysed here combine to give the reader insights that are more than the sum of the book's individual chapters, as surprising similarities become apparent in seemingly disparate and unconnected systems. MTS systems call into question naïve perceptions of time and complexity, moving beyond conventional ways of description, analysis, understanding, modelling, numerical prediction, and prescription of the world around us. This edited collection presents new ways of forecasting, introduces new means of control, and - perhaps as the most demanding task - it singles out a sustainable description of an MTS system under observation, offering a more nuanced interpretation of the floods of quantitative data and images made available by high- and low-frequency measurement tools in our unprecedented era of information flows
Author: Claude Lobry
Publisher: John Wiley & Sons
Published: 2018-07-27
Total Pages: 280
ISBN-13: 1119544017
DOWNLOAD EBOOKBetter known as the "predator-prey relationship," the consumer-resource relationship means the situation where a single species of organisms consumes for survival and reproduction. For example, Escherichia coli consumes glucose, cows consume grass, cheetahs consume baboons; these three very different situations, the first concerns the world of bacteria and the resource is a chemical species, the second concerns mammals and the resource is a plant, and in the final case the consumer and the resource are mammals, have in common the fact of consuming. In a chemostat, microorganisms generally consume (abiotic) minerals, but not always, bacteriophages consume bacteria that constitute a biotic resource. 'The Chemostat' book dealt only with the case of abiotic resources. Mathematically this amounts to replacing in the two equation system of the chemostat the decreasing function by a general increasing then decreasing function. This simple change has greatly enriched the theory. This book shows in this new framework the problem of competition for the same resource.
Author: Zenghu Li
Publisher: Springer Science & Business Media
Published: 2010-11-10
Total Pages: 356
ISBN-13: 3642150047
DOWNLOAD EBOOKMeasure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigration superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups. The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.
Author: D. Alistair Steyn-Ross
Publisher: Springer Science & Business Media
Published: 2010-03-14
Total Pages: 325
ISBN-13: 1441907963
DOWNLOAD EBOOKForeword by Walter J. Freeman. The induction of unconsciousness using anesthetic agents demonstrates that the cerebral cortex can operate in two very different behavioral modes: alert and responsive vs. unaware and quiescent. But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts. Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle. The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states. Modeling Phase Transitions in the Brain contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band Hopf oscillations, gap-junction-moderated Turing structures, and Hopf-Turing interactions leading to cortical waves.
