The Lorenz Equations
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The Lorenz Equations
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Author : Colin Sparrow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Lorenz Equations written by Colin Sparrow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
The Lorenz Equations
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Author : Colin Sparrow
language : en
Publisher:
Release Date : 1982-12-01
The Lorenz Equations written by Colin Sparrow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-12-01 with categories.
Applied Analysis Of The Navier Stokes Equations
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Author : Charles R. Doering
language : en
Publisher: Cambridge University Press
Release Date : 1995
Applied Analysis Of The Navier Stokes Equations written by Charles R. Doering and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The Navier-Stokes equations are a set of nonlinear partial differential equations comprising the fundamental dynamical description of fluid motion. They are applied routinely to problems in engineering, geophysics, astrophysics, and atmospheric science. This book is an introductory physical and mathematical presentation of the Navier-Stokes equations, focusing on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion. Intended for graduate students and researchers in applied mathematics and theoretical physics, results and techniques from nonlinear functional analysis are introduced as needed with an eye toward communicating the essential ideas behind the rigorous analyses.
Dynamical Systems And Numerical Analysis
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Author : A. M. Stuart
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-28
Dynamical Systems And Numerical Analysis written by A. M. Stuart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-28 with Mathematics categories.
The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Nonlinear Dynamics And Chaos In Agricultural Systems
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Author : K. Sakai
language : en
Publisher: Gulf Professional Publishing
Release Date : 2001-06-21
Nonlinear Dynamics And Chaos In Agricultural Systems written by K. Sakai and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-21 with Nature categories.
An introduction to the analysis of chaos for readers majoring in agricultural science and an introduction to agricultural science for readers majoring in mathematical science and other fields. Hopes some readers will pursue further studies on the chaos of arable land. (Pref.)
Nonlinear Partial Differential Equations For Scientists And Engineers
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Author : Lokenath Debnath
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-06
Nonlinear Partial Differential Equations For Scientists And Engineers written by Lokenath Debnath and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-06 with Mathematics categories.
The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.
Introduction To Complexity And Complex Systems
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Author : Robert B. Northrop
language : en
Publisher: CRC Press
Release Date : 2014-10-07
Introduction To Complexity And Complex Systems written by Robert B. Northrop and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-07 with Medical categories.
The boundaries between simple and complicated, and complicated and complex system designations are fuzzy and debatable, even using quantitative measures of complexity. However, if you are a biomedical engineer, a biologist, physiologist, economist, politician, stock market speculator, or politician, you have encountered complex systems. Furthermore
Differential Equations Dynamical Systems And An Introduction To Chaos
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Author : Morris W. Hirsch
language : en
Publisher: Academic Press
Release Date : 2012-03-12
Differential Equations Dynamical Systems And An Introduction To Chaos written by Morris W. Hirsch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-12 with Mathematics categories.
Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems. - Classic text by three of the world's most prominent mathematicians - Continues the tradition of expository excellence - Contains updated material and expanded applications for use in applied studies
Nonlinear Dynamics And Chaos With Student Solutions Manual
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Author : Steven H. Strogatz
language : en
Publisher: CRC Press
Release Date : 2018-09-21
Nonlinear Dynamics And Chaos With Student Solutions Manual written by Steven H. Strogatz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-21 with Mathematics categories.
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.
Dynamical System And Chaos
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Author : Rui Dilão
language : en
Publisher: Springer Nature
Release Date : 2023-04-06
Dynamical System And Chaos written by Rui Dilão and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-06 with Science categories.
This textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful. The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters.