Invariant Sets For Windows

Author : Albert D. Morozov
Publisher : World Scientific
Page : 280 pages
File Size : 52,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9810240716

Get Book

Invariant Sets for Windows by Albert D. Morozov Pdf

This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 96 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book. The book consists of two parts. Part I contains a description of WlnSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical systems to computer design. In Part II, the invariant sets presented in Part I are investigated from the theoretical perspective. The invariant sets of dynamical systems with one, one-and-a-half and two degrees of freedom, as well as those of two-dimensional maps, are discussed. The basic models of the diffusion equations are also considered. This part of the book is intended for a more advanced reader, with at least a BSc in Mathematics.

Author : Gardini Laura,Avrutin Viktor,Sushko Iryna,Tramontana Fabio
Publisher : World Scientific
Page : 648 pages
File Size : 49,5 Mb
Release : 2019-05-28
Category : Mathematics
ISBN : 9789811204715

Get Book

Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures by Gardini Laura,Avrutin Viktor,Sushko Iryna,Tramontana Fabio Pdf

The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.

Author : David Lawrence Rod
Publisher : Unknown
Page : 172 pages
File Size : 52,5 Mb
Release : 1971
Category : Differentiable dynamical systems
ISBN : WISC:89011223997

Get Book

Invariant Sets in the Monkey Saddle by David Lawrence Rod Pdf

Author : Alwyn Scott
Publisher : Routledge
Page : 1107 pages
File Size : 52,7 Mb
Release : 2006-05-17
Category : Reference
ISBN : 9781135455583

Get Book

Encyclopedia of Nonlinear Science by Alwyn Scott Pdf

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Author : Mario Andrea Marchisio
Publisher : Springer
Page : 187 pages
File Size : 41,9 Mb
Release : 2018-05-14
Category : Medical
ISBN : 9789811087523

Get Book

Introduction to Synthetic Biology by Mario Andrea Marchisio Pdf

The textbook is based on the lectures of the course “Synthetic Biology” for Master’s students in biology and biotechnology at the Harbin Institute of Technology. The goal of the textbook is to explain how to make mathematical models of synthetic gene circuits that will, later on, drive the circuit implementation in the lab. Concepts such as kinetics, circuit dynamics and equilibria, stochastic and deterministic simulations, parameter analysis and optimization are presented. At the end of the textbook, a chapter contains a description of structural motifs (e.g. positive and negative feedback loops, Boolean gates) that carry out specific functions and can be combined into larger networks. Moreover, several chapters show how to build up (an analyse, where possible) models for synthetic gene circuits with four different open-source software i.e. COPASI, XPPAUT, BioNetGeN, and Parts & Pools-ProMoT.

Author : Colin Sparrow
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461257677

Get Book

The Lorenz Equations by Colin Sparrow Pdf

The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos", where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity", where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense.

Author : Ying-Cheng Lai,Tamás Tél
Publisher : Springer Science & Business Media
Page : 499 pages
File Size : 45,8 Mb
Release : 2011-02-26
Category : Mathematics
ISBN : 9781441969873

Get Book

Transient Chaos by Ying-Cheng Lai,Tamás Tél Pdf

The aim of this Book is to give an overview, based on the results of nearly three decades of intensive research, of transient chaos. One belief that motivates us to write this book is that, transient chaos may not have been appreciated even within the nonlinear-science community, let alone other scientific disciplines.

Author : Duncan J. MacGregor,Gareth Leng
Publisher : John Wiley & Sons
Page : 340 pages
File Size : 42,8 Mb
Release : 2016-04-18
Category : Medical
ISBN : 9781119951698

Get Book

Computational Neuroendocrinology by Duncan J. MacGregor,Gareth Leng Pdf

Neuroendocrinology with its well defined functions, inputs, and outputs, is one of the most fertile grounds for computational modeling in neuroscience. But modeling is often seen as something of a dark art. This book aims to display the power of modeling approaches in neuroendocrinology, and to showcase its potential for understanding these complex systems. A recurring theme in neuroendocrinology is rhythms. How are rhythms generated, and what purpose do they serve? Are these two questions inextricably intertwined? This book is written for innocents, presuming no math beyond high school or computing beyond calculators. It seeks to lead the curious into the thinking of the modeler, providing the tools to the reader to understand models, and even develop their own, giving life to paper diagrams. The diverse chapters, from ion channels to networks, systems, and hormonal rhythms, each tell the story of a model serving to join the hard won dots of experimentation, mapping a new understanding, and revealing hidden knowledge. • Written by a team of internationally renowned researchers • Both print and enhanced e-book versions are available • Illustrated in full colour throughout This is the fourth volume in a new Series ‘Masterclass in Neuroendocrinology’ , a co- publication between Wiley and the INF (International Neuroendocrine Federation) that aims to illustrate highest standards and encourage the use of the latest technologies in basic and clinical research and hopes to provide inspiration for further exploration into the exciting field of neuroendocrinology. Series Editors: John A. Russell, University of Edinburgh, UK and William E. Armstrong, The University of Tennessee, USA • Written by a team of internationally renowned researchers • Both print and enhanced e-book versions are available • Illustrated in full colour throughout This is the fourth volume in a new Series ‘Masterclass in Neuroendocrinology’ , a co- publication between Wiley and the INF (International Neuroendocrine Federation) that aims to illustrate highest standards and encourage the use of the latest technologies in basic and clinical research and hopes to provide inspiration for further exploration into the exciting field of neuroendocrinology. Series Editors: John A. Russell, University of Edinburgh, UK and William E. Armstrong, The University of Tennessee, USA

Author : Joaquín Delgado,Ernesto A. Lacomba,Jaume Llibre,Ernesto Perez-Chavela
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781441990587

Get Book

New Advances in Celestial Mechanics and Hamiltonian Systems by Joaquín Delgado,Ernesto A. Lacomba,Jaume Llibre,Ernesto Perez-Chavela Pdf

The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celestial Mechanics, Hamiltonian systems and related topics in order to communicate new results and look forward for join research projects. For PhD students, this meeting offered also the opportunity of personal contact to help themselves in their own research, to call as well and promote the attention of young researchers and graduated students from our scientific community to the above topics, which are nowadays of interest and relevance in Celestial Mechanics and Hamiltonian dynamics. A glance to the achievements in the area in the last century came as a consequence of joint discussions in the workshop sessions, new problems were presented and lines of future research were delineated. Specific discussion topics included: New periodic orbits and choreographies in the n-body problem, singularities in few body problems, central configurations, restricted three body problem, geometrical mechanics, dynamics of charged problems, area preserving maps and Arnold diffusion.

Author : F. Axel,F. Denoyer,J.P. Gazeau
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 43,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662042533

Get Book

From Quasicrystals to More Complex Systems by F. Axel,F. Denoyer,J.P. Gazeau Pdf

This book is a collection of part of the written versions of the Physics Courses given at the Winter School "Order, Chance and Risk: Aperiodic Phenomena from Solid State to Finance" held at the Les Houches Center for Physics, between February 23 and March 6, 1998. The School gathered lecturers and participants from all over the world. On a thematic level, the content of the school can be viewed both as a continuation (aperiodic phenomena in solid state physics) and an extension (mathematical aspects of fmance and economy) of the previous "Beyond Quasicrystals", also held at Les Houches, March 7-18 1994 and published in the same ·series. One of its important goals was to promote in-depth concrete scientific exchanges between theoretical physicists, experimental physicists and mathematicians on the one hand, and on the other hand practitioners of the economico-fmancial sphere and specialists of financial mathematics. Therefore, besides the mathematical tools and concepts at work in theoretical descriptions, relevant experimental data were also presented together with methods allowing their interpretation. As a result of this choice, the School was stimulated by experimentalists and fmancial market operators who joined the theoretical physicists and mathematicians at the conference. The present volume deals with the theoretical and experimental studies on aperiodic solids with long range order, incommensurate phases, quasicrystals, glasses, and more complex systems (fractal, chaotic), while a second volume to appear in the same series is devoted to the finance and economy facet.

Author : Yushu Chen,Andrew Y.T. Leung
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781447115755

Get Book

Bifurcation and Chaos in Engineering by Yushu Chen,Andrew Y.T. Leung Pdf

For the many different deterministic non-linear dynamic systems (physical, mechanical, technical, chemical, ecological, economic, and civil and structural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one's perception of numerous non-linear phenomena and laws considerably, together with its great effects on many areas of application. As the important subject matter of non-linear science, bifurcation theory, singularity theory and chaos theory have developed rapidly in the past two or three decades. They are now advancing vigorously in their applications to mathematics, physics, mechanics and many technical areas worldwide, and they will be the main subjects of our concern. This book is concerned with applications of the methods of dynamic systems and subharmonic bifurcation theory in the study of non-linear dynamics in engineering. It has grown out of the class notes for graduate courses on bifurcation theory, chaos and application theory of non-linear dynamic systems, supplemented with our latest results of scientific research and materials from literature in this field. The bifurcation and chaotic vibration of deterministic non-linear dynamic systems are studied from the viewpoint of non-linear vibration.

Author : Erik M. Bollt,Naratip Santitissadeekorn
Publisher : SIAM
Page : 376 pages
File Size : 47,5 Mb
Release : 2013-12-03
Category : Mathematics
ISBN : 9781611972634

Get Book

Applied and Computational Measurable Dynamics by Erik M. Bollt,Naratip Santitissadeekorn Pdf

Until recently, measurable dynamics has been held as a highly theoretical mathematical topic with few generally known obvious links for practitioners in areas of applied mathematics. However, the advent of high-speed computers, rapidly developing algorithms, and new numerical methods has allowed for a tremendous amount of progress and sophistication in efforts to represent the notion of a transfer operator discretely but to high resolution. This book connects many concepts in dynamical systems with mathematical tools from areas such as graph theory and ergodic theory. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures, and transport problems. The new and fast-developing computational tools discussed throughout the book allow for detailed analysis of real-world problems that are simply beyond the reach of traditional methods.

Author : P.H. Rabinowitz,A. Ambrosetti,I. Ekeland,E.J. Zehnder
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400939332

Get Book

Periodic Solutions of Hamiltonian Systems and Related Topics by P.H. Rabinowitz,A. Ambrosetti,I. Ekeland,E.J. Zehnder Pdf

This volume contains the proceedings of a NATO Advanced Research Workshop on Periodic Solutions of Hamiltonian Systems held in II Ciocco, Italy on October 13-17, 1986. It also contains some papers that were an outgrowth of the meeting. On behalf of the members of the Organizing Committee, who are also the editors of these proceedings, I thank all those whose contributions made this volume possible and the NATO Science Committee for their generous financial support. Special thanks are due to Mrs. Sally Ross who typed all of the papers in her usual outstanding fashion. Paul H. Rabinowitz Madison, Wisconsin April 2, 1987 xi 1 PERIODIC SOLUTIONS OF SINGULAR DYNAMICAL SYSTEMS Antonio Ambrosetti Vittorio Coti Zelati Scuola Normale Superiore SISSA Piazza dei Cavalieri Strada Costiera 11 56100 Pisa, Italy 34014 Trieste, Italy ABSTRACT. The paper contains a discussion on some recent advances in the existence of periodic solutions of some second order dynamical systems with singular potentials. The aim of this paper is to discuss some recent advances in th.e existence of periodic solutions of some second order dynamical systems with singular potentials.

Author : Michael Wayne
Publisher : Bloomsbury Publishing
Page : 208 pages
File Size : 51,5 Mb
Release : 2014-09-25
Category : Philosophy
ISBN : 9781472508683

Get Book

Red Kant: Aesthetics, Marxism and the Third Critique by Michael Wayne Pdf

Is Kant really the 'bourgeois' philosopher that his advocates and opponents take him to be? In this bold and original re-thinking of Kant, Michael Wayne argues that with his aesthetic turn in the Third Critique, Kant broke significantly from the problematic philosophical structure of the Critique of Pure Reason. Through his philosophy of the aesthetic Kant begins to circumnavigate the dualities in his thought. In so doing he shows us today how the aesthetic is a powerful means for imagining our way past the apparent universality of contemporary capitalism. Here is an unfamiliar Kant: his concepts of beauty and the sublime are reinterpreted as attempts to socialise the aesthetic while Wayne reconstructs the usually hidden genealogy between Kant and important Marxist concepts such as totality, dialectics, mediation and even production. In materialising Kant's philosophy, this book simultaneously offers a Marxist defence of creativity and imagination grounded in our power to think metaphorically and in Kant's concept of reflective judgment. Wayne also critiques aspects of Marxist cultural theory that have not accorded the aesthetic the relative autonomy and specificity which it is due. Discussing such thinkers as Adorno, Bourdieu, Colletti, Eagleton, Lukács, Ranciére and others, Red Kant: Aesthetics, Marxism and the Third Critique presents a new reading of Kant's Third Critique that challenges Marxist and mainstream assessments of Kant alike.

Author : Bard Ermentrout
Publisher : SIAM
Page : 304 pages
File Size : 46,9 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0898718198

Get Book

Simulating, Analyzing, and Animating Dynamical Systems by Bard Ermentrout Pdf

Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modeling techniques and methods for analyzing the resulting equations.