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Author : Hau Lin
Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.:/5 (253 download)
Download or read book Dynamics and Chaotic Behavior of a Chemostat written by Hau Lin and published by . This book was released on 1989 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Abdelhamid Ajbar
Publisher : CRC Press
ISBN 13 : 1439867143
Total Pages : 370 pages
Book Rating : 4.4/5 (398 download)
Download or read book Dynamics of the Chemostat written by Abdelhamid Ajbar and published by CRC Press. This book was released on 2011-08-09 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ubiquitous tool in mathematical biology and chemical engineering, the chemostat often produces instabilities that pose safety hazards and adversely affect the optimization of bioreactive systems. Singularity theory and bifurcation diagrams together offer a useful framework for addressing these issues. Based on the authors’ extensive work in this field, Dynamics of the Chemostat: A Bifurcation Theory Approach explores the use of bifurcation theory to analyze the static and dynamic behavior of the chemostat. Introduction The authors first survey the major work that has been carried out on the stability of continuous bioreactors. They next present the modeling approaches used for bioreactive systems, the different kinetic expressions for growth rates, and tools, such as multiplicity, bifurcation, and singularity theory, for analyzing nonlinear systems. Application The text moves on to the static and dynamic behavior of the basic unstructured model of the chemostat for constant and variable yield coefficients as well as in the presence of wall attachment. It then covers the dynamics of interacting species, including pure and simple microbial competition, biodegradation of mixed substrates, dynamics of plasmid-bearing and plasmid-free recombinant cultures, and dynamics of predator–prey interactions. The authors also examine dynamics of the chemostat with product formation for various growth models, provide examples of bifurcation theory for studying the operability and dynamics of continuous bioreactor models, and apply elementary concepts of bifurcation theory to analyze the dynamics of a periodically forced bioreactor. Using singularity theory and bifurcation techniques, this book presents a cohesive mathematical framework for analyzing and modeling the macro- and microscopic interactions occurring in chemostats. The text includes models that describe the intracellular and operating elements of the bioreactive system. It also explains the mathematical theory behind the models.
Author : Abdelhamid Ajbar
Publisher : CRC Press
ISBN 13 : 143986716X
Total Pages : 366 pages
Book Rating : 4.4/5 (398 download)
Download or read book Dynamics of the Chemostat written by Abdelhamid Ajbar and published by CRC Press. This book was released on 2011-08-09 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ubiquitous tool in mathematical biology and chemical engineering, the chemostat often produces instabilities that pose safety hazards and adversely affect the optimization of bioreactive systems. Singularity theory and bifurcation diagrams together offer a useful framework for addressing these issues. Based on the authors' extensive work in this
Author : T. Bountis
Publisher : Springer Science & Business Media
ISBN 13 : 146153464X
Total Pages : 410 pages
Book Rating : 4.4/5 (615 download)
Download or read book Chaotic Dynamics written by T. Bountis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many conferences, meetings, workshops, summer schools and symposia on nonlinear dynamical systems are being organized these days, dealing with a great variety of topics and themes -classical and quantum, theoretical and experimental. Some focus on integrability, or discuss the mathematical foundations of chaos. Others explore the beauty of fractals, or examine endless possibilities of applications to problems of physics, chemistry, biology and other sciences. A new scientific discipline has thus emerged, with its own distinct philosophical viewpoint and an impressive arsenal of new methods and techniques, which may be called Chaotic Dynamics. Perhaps its most outstanding achievement so far has been to shed new light on many long standing issues involving complicated, irregular or "chaotic" nonlinear phenomena. The concepts of randomness, complexity and unpredictability have been critically re-examined and the fundamental importance of scaling, self-similarity and sensitive dependence on parameters and initial conditions has been firmly established. In this NATO ASI, held at the seaside Greek city of Patras, between July 11- 20, 1991, a serious effort was made to bring together scientists representing many of the different aspects of Chaotic Dynamics. Our main aim was to review recent advances, evaluate the current state of the art and identify some of the more promising directions for research in Chaotic Dynamics.
Author : S. Koga
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (131 download)
Download or read book Study of the Dynamic Behavior of the Chemostat System written by S. Koga and published by . This book was released on 1967 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Milos Marek
Publisher : Cambridge University Press
ISBN 13 : 9780521438308
Total Pages : 384 pages
Book Rating : 4.4/5 (383 download)
Download or read book Chaotic Behaviour of Deterministic Dissipative Systems written by Milos Marek and published by Cambridge University Press. This book was released on 1995-07-20 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate text surveys both the theoretical and experimental aspects of deterministic chaotic behaviour.
Author : Gregory L. Baker
Publisher : Cambridge University Press
ISBN 13 : 9780521471060
Total Pages : 282 pages
Book Rating : 4.4/5 (71 download)
Download or read book Chaotic Dynamics written by Gregory L. Baker and published by Cambridge University Press. This book was released on 1996 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.
Author : Elhadj Zeraoulia
Publisher : World Scientific
ISBN 13 : 9814340693
Total Pages : 268 pages
Book Rating : 4.8/5 (143 download)
Download or read book Frontiers in the Study of Chaotic Dynamical Systems with Open Problems written by Elhadj Zeraoulia and published by World Scientific. This book was released on 2011 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of fascinating topics of current interest and problems arising in the study of both discrete and continuous time chaotic dynamical systems. Exciting new techniques stemming from the area of nonlinear dynamical systems theory are currently being developed to meet these challenges. Presenting the state-of-the-art of the more advanced studies of chaotic dynamical systems, Frontiers in the Study of Chaotic Dynamical Systems with Open Problems is devoted to setting an agenda for future research in this exciting and challenging field.
Author : J. Thanh Van Tran
Publisher : Atlantica Séguier Frontières
ISBN 13 : 9782863321584
Total Pages : 368 pages
Book Rating : 4.3/5 (215 download)
Download or read book Chaos and Complexity written by J. Thanh Van Tran and published by Atlantica Séguier Frontières. This book was released on 1995 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tomasz Kapitaniak
Publisher : World Scientific
ISBN 13 : 9789810204105
Total Pages : 256 pages
Book Rating : 4.2/5 (41 download)
Download or read book Chaos in Systems with Noise written by Tomasz Kapitaniak and published by World Scientific. This book was released on 1990 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the first edition, the influence of random noise on the chaotic behavior of dissipative dynamical systems is investigated. Problems are illustrated by mechanical examples. This revised and updated edition contains new sections on the summary of probability theory, homoclinic chaos, Melnikov method, routes to chaos, stabilization of period-doubling, and Hopf bifurcation by noise. Some chapters have been rewritten and new examples have been added.
Author : Gérard Iooss
Publisher : North-Holland
ISBN 13 :
Total Pages : 752 pages
Book Rating : 4.3/5 (91 download)
Download or read book Chaotic Behaviour of Deterministic Systems written by Gérard Iooss and published by North-Holland. This book was released on 1983 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Angelo Vulpiani
Publisher : World Scientific
ISBN 13 : 9814277665
Total Pages : 482 pages
Book Rating : 4.8/5 (142 download)
Download or read book Chaos written by Angelo Vulpiani and published by World Scientific. This book was released on 2010 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
Author : Christophe Letellier
Publisher : World Scientific
ISBN 13 : 9814434868
Total Pages : 362 pages
Book Rating : 4.8/5 (144 download)
Download or read book Topology and Dynamics of Chaos written by Christophe Letellier and published by World Scientific. This book was released on 2013 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,
Author : Dmytro Vavriv
Publisher : Cuvillier Verlag
ISBN 13 : 373693159X
Total Pages : 94 pages
Book Rating : 4.7/5 (369 download)
Download or read book Chaotic instabilities and their applications written by Dmytro Vavriv and published by Cuvillier Verlag. This book was released on 2009-11-18 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The phenomenon of chaos, which is arising as noise-like oscillations in deterministic low-dimensional nonlinear system–s, should be treated from two different points of view. First, this effect can create a threat to stability of many practical systems, and it is needed to know conditions for the chaos to arise. Second, chaotic oscillations can be used for the development of various advanced devices, like noise oscillators, random number generators, noise radars, and so on. Both mentioned directions of the chaos study are addressed in this thesis. In this thesis, we present a first attempt to study chaotic instabilities which arise during the transition of pulses via nonlinear circuits. The mathematical model used is a generalized Duffing equation, which is an adequate model to describe stability in a number of electronic, microwave, and optical devices. The simplest physical oscillator which is described by such equation is a RLC-circuit with nonlinear capacitor, or a cavity with nonlinear element or media. Analytical, numerical, and experimental methods have been used in order to determine conditions for chaotic instabilities arising. For example, the application of secondary averaging has enabled us to find resonances which can give rise to chaotic instabilities, and to determine analytical conditions for chaos onset. These conditions have been compared with those obtained from numerical simulations and experimental investigations, and a good correspondence of the obtained results has been detected. The experiments have been performed with a nonlinear RLC circuit forced by a train of RF-pulses with rectangular envelope and with carrier frequency of about 30 MHz. The obtained results indicate that weakly nonlinear oscillators which are stable under harmonic forcing can lose their stability when a train of pulses is applied. The development of the chaotic instabilities takes place due to the interaction of spectral components of the pulse train. It is shown that there is a certain relation between the pulse duration and the pulse period when the threshold for chaos with respect to pulse intensity reaches a minimum value. This value is also lowering with reduced losses in the system and with increased the period of modulation and the nonlinearity parameter. The second part of the thesis is devoted to the application of chaotic oscillations for the development of reliable sources of random sequences. We have presented a proof that chaotic oscillations generated by some nonlinear systems can be used to produce random binary sequences. These sequences pass the tests specified by the US Standard FIPS PUB 140-1/140-2, and this means that they are suitable for cryptographic applications. Generators of random sequences based on deterministic systems with chaotic behaviour, like physical noise sources, can generate truly random sequences in opposite to software generators, which produce pseudorandom cycle samples. We have also determined regularities of the formation of chaotic oscillations, which can be used for the production of random binary sequences. In particular, it has been detected that the areas of existence of chaotic oscillations in the control parameter space are wider as compared to those areas, where random sequences are produced. Hence, not any chaos generation scheme can be used for the production of random sequences. Moreover, it turned out that not any dynamical system with chaotic behavior is suitable for this purpose. For example, the forced pendulum generates sequences which do not pass the tests for randomness. The most possible reason for not passing the tests is related with the presence of intensive spectral components in the power spectrum. However, the presented results of the study of the Lorenz equations and a pendulum equation with delay as well as the Mackey-Glass equation indicate that it is possible to find dynamical systems with chaotic behavior, which generate random sequences in wide areas of their control parameters. The obtained results clearly indicate that deterministic systems with chaotic behavior can be used as generators of random sequences combining the advantages of software random generators and physical noise sources.
Author : Yurii Bolotin
Publisher : Springer
ISBN 13 : 9783319825922
Total Pages : 281 pages
Book Rating : 4.8/5 (259 download)
Download or read book Chaos: Concepts, Control and Constructive Use written by Yurii Bolotin and published by Springer. This book was released on 2018-06-28 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.
Author : Neal B Abraham
Publisher :
ISBN 13 : 9781475706246
Total Pages : 488 pages
Book Rating : 4.7/5 (62 download)
Download or read book Measures of Complexity and Chaos written by Neal B Abraham and published by . This book was released on 1990-06-30 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Fielding Barnsley
Publisher :
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.3/5 (91 download)
Download or read book Chaotic Dynamics and Fractals written by Michael Fielding Barnsley and published by . This book was released on 1986 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaotic Dynamics and Fractals.
