Download or read book Qualitative Analysis of the Periodically Forced Relaxation Oscillations written by Mark Levi and published by American Mathematical Soc.. This book was released on 1981 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book MicroRNA Regulatory Network Structure and Function written by Zengrong Liu and published by Springer. This book was released on 2018-11-02 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses topics related to the topological structure and biological function of gene networks regulated by microRNAs. It focuses on analyzing the relation between topological structure and biological function, applying these theoretical results to gene networks involving microRNA, illustrating their biological mechanisms, and identifying the roles of microRNA in controlling various phenomena emerging from the networks. In addition, the book explains how to control the complex biological phenomena using mathematical tools and offers a new perspective on studying microRNA. It is a useful resource for graduate students and researchers who are working on or interested in microRNAs and gene network.
Download or read book Nonlinearity in Condensed Matter written by Alan R. Bishop 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: The Sixth Annual Conference of the Center for Nonlinear Studies at the Los Alamos National Laboratory was held May 5-9, 1986, on the topic "Nonlinearity in Condensed Matter: Lessons from the Past and Prospects for the Future. " As conference organizers, we felt that the study of non linear phenomena in condensed matter had matured to the point where it made sense to take stock of the numerous lessons to be learned from a variety of contexts where nonlinearity plays a fundamental role and to evaluate the prospects for the growth of this general discipline. The successful 1978 Oxford Symposium on nonlinear (soliton) struc ture and dynamics in condensed matter (Springer Ser. Solid-State Sci. , Vol. 8) was held at a time when the ubiquity of solitons was just begin ning to be appreciated by the condensed matter community; in subsequent years the soliton paradigm has provided a rather useful framework for in vestigating a large number of phenomena, particularly in low-dimensional systems. Nevertheless, we felt that the importance of nonlinearity in wider arenas than "solitonics" merited a significant expansion in the scope of the conference over that of the 1978 symposium. Indeed, many of the lessons are quite general and their potential for cross-fertilization of otherwise poorly connected disciplines was certainly one of the prime motivations for this conference. Thus, while these proceedings contain many contribu tions pertaining to soliton behavior in different contexts, the reader will find much more as well, particularly in the later chapters.
Download or read book Nonlinear Dynamics and Chaos written by J. M. T. Thompson and published by John Wiley & Sons. This book was released on 2002-02-15 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ein angesehener Bestseller - jetzt in der 2.aktualisierten Auflage! In diesem Buch finden Sie die aktuellsten Forschungsergebnisse auf dem Gebiet nichtlinearer Dynamik und Chaos, einem der am schnellsten wachsenden Teilgebiete der Mathematik. Die seit der ersten Auflage hinzugekommenen Erkenntnisse sind in einem zusätzlichen Kapitel übersichtlich zusammengefasst.
Download or read book Chaos written by Arun V. Holden and published by Princeton University Press. This book was released on 2014-07-14 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as chaotic processes. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Continuum Theory and Dynamical Systems written by Morton Brown and published by American Mathematical Soc.. This book was released on 1991 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Relationships between Continuum Theory and the Theory of Dynamical Systems, held at Humboldt State University in Arcata, California in June 1989. The conference reflected recent interactions between dynamical systems and continuum theory. Illustrating the increasing confluence of these two areas, this volume contains introductory papers accessible to mathematicians and graduate students in any area of mathematics, as well as papers aimed more at specialists. Most of the papers are concerned with the dynamics of surface homeomorphisms or of continua that occur as attractors for surface homeomorphisms.
Download or read book Combinatorial Dynamics And Entropy In Dimension One 2nd Edition written by Luis Alseda and published by World Scientific Publishing Company. This book was released on 2000-10-31 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of “chaos” present in it; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself.
Download or read book Attractors Bifurcations and Chaos written by Tönu Puu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.
Download or read book Global Theory of Dynamical Systems written by Z. Nitecki and published by Springer. This book was released on 2006-11-14 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Replication of Chaos in Neural Networks Economics and Physics written by Marat Akhmet and published by Springer. This book was released on 2015-08-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
Download or read book Nonlinear Economic Dynamics written by Tönu Puu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was first pUblished in 1989 as volume 336 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and it reappeared in a 2nd edition as a Springer monograph in 1991. After considerable revisions it appeared in a 3rd edition in 1993. The origin, still visible in the 3rd edition, was the joint work of the author with Professor Martin J. Beckmann, documented in two co-authored mono graphs "Spatial Economics" (North-Holland 1985), and "Spatial Structures" (Springer-Verlag 1990). Essential dynamics had, however, been almost com pletely lacking in these works, and the urge to focus the dynamic issues was great. To fill this particular gap was the aim of the previous editions, and so the spatial aspect provided core and focus. In the present edition a substantial quantity of spatial issues have been removed: All those that were dynamic only in the sense that structures were characterized which were structurally stable, or robust in a changing world. The removed material has meanwhile been published as a separate mono graph under the title "Mathematical Location and Land Use Theory" (Springer-Verlag 1996).
Download or read book Collisions Rings and Other Newtonian N Body Problems written by Donald Saari and published by American Mathematical Soc.. This book was released on 2005 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth chapter analyzes collisions, while the last chapter discusses the likelihood of collisions and other events."--Jacket.
Download or read book Elegant Chaos written by Julien C. Sprott and published by World Scientific. This book was released on 2010 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Fundamentals. 1.1. Dynamical systems. 1.2. State space. 1.3. Dissipation. 1.4. Limit cycles. 1.5. Chaos and strange attractors. 1.6. Poincaré sections and fractals. 1.7. Conservative chaos. 1.8. Two-toruses and quasiperiodicity. 1.9. Largest Lyapunov exponent. 1.10. Lyapunov exponent spectrum. 1.11. Attractor dimension. 1.12. Chaotic transients. 1.13. Intermittency. 1.14. Basins of attraction. 1.15. Numerical methods. 1.16. Elegance -- 2. Periodically forced systems. 2.1. Van der Pol oscillator. 2.2. Rayleigh oscillator. 2.3. Rayleigh oscillator variant. 2.4. Duffing oscillator. 2.5. Quadratic oscillators. 2.6. Piecewise-linear oscillators. 2.7. Signum oscillators. 2.8. Exponential oscillators. 2.9. Other undamped oscillators. 2.10. Velocity forced oscillators. 2.11. Parametric oscillators. 2.12. Complex oscillators -- 3. Autonomous dissipative systems. 3.1. Lorenz system. 3.2. Diffusionless Lorenz system. 3.3. Rs̈sler system. 3.4. Other quadratic systems. 3.5. Jerk systems. 3.6. Circulant systems. 3.7. Other systems -- 4. Autonomous Conservative Systems. 4.1. Nosé-Hoover oscillator. 4.2. Nosé-Hoover variants. 4.3. Jerk systems. 4.4. Circulant systems -- 5. Low-dimension systems (D3). 5.1. Dixon system. 5.2. Dixon variants. 5.3. Logarithmic case. 5.4. Other cases -- 6. High-dimensional systems (D3). 6.1. Periodically forced systems. 6.2. Master-slave oscillators. 6.3. Mutually coupled nonlinear oscillators. 6.4. Hamiltonian systems. 6.5. Anti-Newtonian systems. 6.6. Hyperjerk systems. 6.7. Hyperchaotic systems. 6.8. Autonomous complex systems. 6.9. Lotka-Volterra systems. 6.10. Artificial neural networks -- 7. Circulant systems. 7.1. Lorenz-Emanuel system. 7.2. Lotka-Volterra systems. 7.3. Antisymmetric quadratic system. 7.4. Quadratic ring system. 7.5. Cubic ring system. 7.6. Hyperlabyrinth system. 7.7. Circulant neural networks. 7.8. Hyperviscous ring. 7.9. Rings of oscillators. 7.10. Star systems -- 8. Spatiotemporal systems. 8.1. Numerical methods. 8.2. Kuramoto-Sivashinsky equation. 8.3. Kuramoto-Sivashinsky variants. 8.4. Chaotic traveling waves. 8.5. Continuum ring systems. 8.6. Traveling wave variants -- 9. Time-delay systems. 9.1. Delay differential equations. 9.2. Mackey-Glass equation. 9.3. Ikeda DDE. 9.4. Sinusoidal DDE. 9.5. Polynomial DDE. 9.6. Sigmoidal DDE. 9.7. Signum DDE. 9.8. Piecewise-linear DDEs. 9.9. Asymmetric logistic DDE with continuous delay -- 10. Chaotic electrical circuits. 10.1. Circuit elegance. 10.2. Forced relaxation oscillator. 10.3. Autonomous relaxation oscillator. 10.4. Coupled relaxation oscillators. 10.5. Forced diode resonator. 10.6. Saturating inductor circuit. 10.7. Forced piecewise-linear circuit. 10.8. Chua's circuit. 10.9. Nishio's circuit. 10.10. Wien-bridge oscillator. 10.11. Jerk circuits. 10.12. Master-slave oscillator. 10.13. Ring of oscillators. 10.14. Delay-line oscillator
Download or read book Noise Induced Transitions written by W. Horsthemke and published by Springer Science & Business Media. This book was released on 2006-09-12 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of phase transitions is among the most fascinating fields in physics. Originally limited to transition phenomena in equilibrium systems, this field has outgrown its classical confines during the last two decades. The behavior of far from equilibrium systems has received more and more attention and has been an extremely active and productive subject of research for physicists, chemists and biologists. Their studies have brought about a more unified vision of the laws which govern self-organization processes of physico-chemical and biological sys tems. A major achievement has been the extension of the notion of phase transi tion to instabilities which occur only in open nonlinear systems. The notion of phase transition has been proven fruitful in apphcation to nonequilibrium ins- bihties known for about eight decades, like certain hydrodynamic instabilities, as well as in the case of the more recently discovered instabilities in quantum optical systems such as the laser, in chemical systems such as the Belousov-Zhabotinskii reaction and in biological systems. Even outside the realm of natural sciences, this notion is now used in economics and sociology. In this monograph we show that the notion of phase transition can be extend ed even further. It apphes also to a new class of transition phenomena which occur only in nonequilibrium systems subjected to a randomly fluctuating en vironment.
Download or read book Dynamical Properties of Diffeomorphisms of the Annulus and of the Torus written by Patrice Le Calvez and published by American Mathematical Soc.. This book was released on 2000 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The second chapter generalizes some aspects of Aubry-Mather theory to such maps and presents a version of the Poincare-Birkhoff theorem in which the periodic orbits have the same braid type as in the linear case. A diffeomorphism of the torus isotopic to the identity is also a composition of twist maps, and it is possible to obtain a proof of the Conley-Zehnder theorem with the same kind of conclusions about the braid type, in the case of periodic orbits. This results leads to an equivariant version of the Brouwer translation theorem which permits new proofs of some results about the rotation set of diffeomorphisms of the torus."--BOOK JACKET.
Download or read book Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations written by Jacob Palis Júnior and published by Cambridge University Press. This book was released on 1995-01-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.
