Stochastic Nonlinear Systems in Physics, Chemistry, and Biology
Stochastic Nonlinear Systems in Physics, Chemistry, and Biology

Author: L. Arnold

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 239

ISBN-13: 3642680380

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This book contains the invited papers of the interdisciplinary workshop on "Stochastic Nonlinear Systems in Physics, Chemistry and Biology" held at the Center for Interdisciplinary Research (ZIF), University of Bielefeld, West Germany, October 5-11, 1980. The workshop brought some 25 physicists, chemists, and biologists - who deal with stochastic phenomena - and about an equal number of mathematicians - who are experts in the theory of stochastic processes - together. The Scientific Commitee consisted of L. Arnold (Bremen), A. Dress (Bielefeld), W. Horsthemke (Brussels), T. Kurtz (Madison), R. Lefever (Brussels), G. Nicolis (Brussels), and V. Wihstutz (Bremen). The main topics of the workshop were the transition from deterministic to stoch astic behavior, external noise and noise induced transitions, internal fluctuations, phase transitions, and irreversible thermodynamics, and on the mathematical side, approximation of stochastic processes, qualitative theory of stochastic systems, and space-time processes. The workshop was sponsored by ZIF, Bielefeld, and by the Universities of Bremen and Brussels. We would like to thank the staff of ZIF and H. Crauel and M. Ehrhardt (Bremen) for the perfect organization and their assistance. In addition, our thanks go to Professor H. Haken for having these Proceedings included in the Se ries in Synergetics. Bremen and Brussels L. Arnold and R. Lefever December 1980 v Contents Part I. Introduction: From Deterministic to Stochastic Behavior On the Foundations of Kinetic Theory By B. Misr~ and I. Prigogine (With 1 Figure) ............................. .

Stochastic Processes in Physics, Chemistry, and Biology
Stochastic Processes in Physics, Chemistry, and Biology

Author: Jan A. Freund

Publisher: Springer

Published: 2008-01-11

Total Pages: 512

ISBN-13: 3540453962

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The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until - cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences - especially chemistry and biology - based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise-- hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.

Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Stochastic Chemical Reaction Systems in Biology
Stochastic Chemical Reaction Systems in Biology

Author: Hong Qian

Publisher: Springer Nature

Published: 2021-10-18

Total Pages: 364

ISBN-13: 3030862526

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This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.

Information Systems Analysis and Modeling
Information Systems Analysis and Modeling

Author: Vladimir S. Lerner

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 329

ISBN-13: 1461546397

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Informational Macrodynamics (IMD) presents the unified information systemic approach with common information language for modeling, analysis and optimization of a variety of interactive processes, such as physical, biological, economical, social, and informational, including human activities. Comparing it with thermodynamics, which deals with transformation energy and represents a theoretical foundation of physical technology, IMD deals with transformation information, and can be considered a theoretical foundation of Information Computer Technology (ICT). ICT includes but is not limited to applied computer science, computer information systems, computer and data communications, software engineering, and artificial intelligence. In ICT, information flows from different data sources, and interacts to create new information products. The information flows may interact physically or via their virtual connections, initiating an information dynamic process that can be distributed in space. As in physics, a problem is understanding general regularities of the information processes in terms of information law, for the engineering and technological design, control, optimization, and development of computer technology, operations, manipulations, and management of real information objects. Information Systems Analysis and Modeling: An Informational Macrodynamics Approach belongs to an interdisciplinary science that represents the new theoretical and computer-based methodology for system informational description and improvement, including various activities in such interdisciplinary areas as thinking, intelligent processes, management, and other nonphysical subjects with their mutual interactions, informational superimpositions, and the information transferred between interactions. Information Systems Analysis and Modeling: An Informational Macrodynamics Approach can be used as a textbook or secondary text in courses on computer science, engineering, business, management, education, and psychology and as a reference for research and industry.

Physics of Bioenergetic Processes
Physics of Bioenergetic Processes

Author: L. A. Blumenfeld

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 141

ISBN-13: 3642685250

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According to its definition, synergetics is concerned with the cooperation of indi vidual parts of a system that produces macroscopic temporal, spatial or functional structures. A good deal of the volumes published within this series dealt with the formation of truly macroscopic structures which we can s. ee with our eyes. A common scheme could be developed to understand the formation of many patterns through self-organization. In particular, we have to use concepts which go beyond conventio nal thermodynamics. New ideas became crucial. We have to study kinetic processes, and often few highly excited degrees of freedom play the decisive role in the evo lution of structures. Over the past years it has turned out that quite similar lines of approach apply to a world which at first sight would be classified as "microsco pic". That world consists of processes in which biomolecules are involved. An impor tant example for the problems occurring there is provided by Manfred Eigen's theory of evolution of life at the molecular level (cf. his contribution to Volume 17 of this series). Another important example has been provided by Blumenfeld's book on problems of biological physics (Vol. 7 of this series). There it was proposed to treat biological molecules as machines which, in a certain sense, work through "macros copic" degrees of freedom.

Evolution of Order and Chaos
Evolution of Order and Chaos

Author: Hermann Haken

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 294

ISBN-13: 364268808X

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These proceedings contain the invited lectures presented at the International Sym posium on Synergetics at Schloss Elmau in April, 1982. This symposium marked the th 10 anniversary of symposia on synergetics, the first of which was held at Schloss Elmau in 1972. As is now weIl known, these symposia are devoted to the study of the formation of structures in physical systems far from thermal equilibrium, as weIl as in nonphysical systems such as those in biology and sociology. While the first proceedings were published by Teubner Publishing Company in 1973 and the second by North Holland Publishing Company in 1974, the subsequent proceed ings have been published in the Springer Series in Synergetics. I believe that these proceedings give a quite faithful picture of the developments in this new interdisciplinary field over the past decade. As H.J. Queisser recently noted, the prefix "non", which is used quite frequent ly in modern scientific literature in words such as "nonequilibrium", "nonlinear", etc., indicates a new development in scientific thinking. Indeed, this new develop ment was anticipated and given a framework in the introduction of "synergetics" more than a decade ago.

Synergetics — From Microscopic to Macroscopic Order
Synergetics — From Microscopic to Macroscopic Order

Author: E. Frehland

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 265

ISBN-13: 364269540X

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This volume contains the papers presented at the International Symposium on "Synergetics - From Microscopic to Macroscopic Order", held at the Wissenschafts kolleg z~ Berlin (Institute for Advanced Study Berlin), on July 4-8, 1983. Further more, it contains a contribution of T. Ohta, who unfortunately could not partici pate in this meeting, on the evolution of mUltigene families. The papers discuss the evolution and the function of ordered structures from small microscopic scales up to large macroscopic dimensions. On the one hand, these structures derive from physical or biological systems; on the other hand, they also affect economic, sociological and philosophical questions. I would like to thank the Wissenschaftskolleg zu Berlin for the extraordinary support and hospitality during my one year's stay there as a fellow, which made the planning, preparation and organization of this symposium possible. I would also like to acknowledge the work of B. Fritsch and D. Dorner who actively participated in this undertaking. I am grateful to Professor Haken, the founder of synergetics, whose participation in the planning and styling of the concept of the conference was essential. I am especially thankful to Mrs. U. Monigatti for her indefatigable help with the prep aration and organization of the conference. The financial support was provided by the "Deutsche Forschungsgemeinschaft". Berlin, November 1983 E. Frehland Contents Some Introductory Remarks on Synergetics By H. Haken ...