With Applications to Physics, Biology, Chemistry, and Engineering
Author: Steven H. Strogatz
Publisher: Hachette UK
ISBN: 0813349117
Category: Mathematics
Page: 500
View: 2585
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. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory. In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.
An Introduction To Chaotic Dynamical Systems
Author: Robert Devaney
Publisher: Westview Press
ISBN: 0786722673
Category: Science
Page: 416
View: 9970
Nonlinear Dynamics and Chaos, 2nd ed. SET with Student Solutions Manual
Author: Steven H. Strogatz
Publisher: Westview Press
ISBN: 9780813350844
Category: Mathematics
Page: 932
View: 7192
Chaos and Nonlinear Dynamics
An Introduction for Scientists and Engineers
Author: Robert C. Hilborn
Publisher: Oxford University Press on Demand
ISBN: 9780198507239
Category: Mathematics
Page: 650
View: 1237
This is a comprehensive introduction to the exciting scientific field of nonlinear dynamics for students, scientists, and engineers, and requires only minimal prerequisites in physics and mathematics. The book treats all the important areas in the field and provides an extensive and up-to-date bibliography of applications in all fields of science, social science, economics, and even the arts.
Author: Robert C. Hilborn
Publisher: Oxford University Press on Demand
ISBN: 9780198507239
Category: Mathematics
Page: 650
View: 1237
Chaos in Dynamical Systems
Author: Edward Ott
Publisher: Cambridge University Press
ISBN: 9780521010849
Category: Mathematics
Page: 478
View: 2965
Student Solutions Manual for Nonlinear Dynamics and Chaos, 2nd edition
Author: Mitchal Dichter
Publisher: CRC Press
ISBN: 0429972636
Category: Mathematics
Page: 404
View: 3941
Dynamics Of Complex Systems
Author: Yaneer Bar-yam
Publisher: Westview Press
ISBN: 9780813341217
Category: Science
Page: 864
View: 7704
Understanding Nonlinear Dynamics
Author: Daniel Kaplan,Leon Glass
Publisher: Springer Science & Business Media
ISBN: 9780387944401
Category: Mathematics
Page: 420
View: 2790
Introduction to Applied Nonlinear Dynamical Systems and Chaos
Author: Stephen Wiggins
Publisher: Springer Science & Business Media
ISBN: 0387217495
Category: Mathematics
Page: 844
View: 8104
An Introduction to Dynamical Systems and Chaos
Author: G.C. Layek
Publisher: Springer
ISBN: 8132225562
Category: Mathematics
Page: 622
View: 1261
Exploring Chaos
Theory And Experiment
Author: Brian Davies
Publisher: CRC Press
ISBN: 0429982496
Category: Mathematics
Page: 256
View: 4775
This book presents elements of the theory of chaos in dynamical systems in a framework of theoretical understanding coupled with numerical and graphical experimentation. The theory is developed using only elementary calculus and algebra, and includes dynamics of one-and two-dimensional maps, periodic orbits, stability and its quantification, chaotic behavior, and bifurcation theory of one-dimensional systems. There is an introduction to the theory of fractals, with an emphasis on the importance of scaling, and a concluding chapter on ordinary differential equations. The accompanying software, written in Java, is available online (see link below). The program enables students to carry out their own quantitative experiments on a variety of nonlinear systems, including the analysis of fixed points of compositions of maps, calculation of Fourier spectra and Lyapunov exponents, and box counting for two-dimensional maps. It also provides for visualizing orbits, final state and bifurcation diagrams, Fourier spectra and Lyapunov exponents, basins of attractions, three-dimensional orbits, Poincarections, and return maps. Please visit http://www.maths.anu.edu.au/~briand/chaos/ for the integrated cross-platform software.
Author: Brian Davies
Publisher: CRC Press
ISBN: 0429982496
Category: Mathematics
Page: 256
View: 4775
Chaos
An Introduction to Dynamical Systems
Author: Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher: Springer
ISBN: 3642592813
Category: Mathematics
Page: 603
View: 5081
BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.
Author: Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher: Springer
ISBN: 3642592813
Category: Mathematics
Page: 603
View: 5081
Sync
How Order Emerges from Chaos In the Universe, Nature, and Daily Life
Author: Steven H. Strogatz
Publisher: Hachette Books
ISBN: 140130446X
Category: Science
Page: 352
View: 6728
At the heart of the universe is a steady, insistent beat, the sound of cycles in sync. Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing.
Author: Steven H. Strogatz
Publisher: Hachette Books
ISBN: 140130446X
Category: Science
Page: 352
View: 6728
Nonlinear Dynamics and Chaos in Agricultural Systems
Author: Kenshi Sakai
Publisher: Gulf Professional Publishing
ISBN: 9780444506467
Category: Mathematics
Page: 204
View: 9121
Chaos in Real Data
The Analysis of Non-Linear Dynamics from Short Ecological Time Series
Author: Joe Perry
Publisher: Springer Science & Business Media
ISBN: 9780412796906
Category: Mathematics
Page: 225
View: 6106
Chaos in Real Data studies the range of data analytic techniques available to study nonlinear population dynamics for ecological time series. Several case studies are studied using typically short and noisy population data from field and laboratory. A range of modern approaches, such as response surface methodology and mechanistic mathematical modelling, are applied to several case studies. Experts honestly appraise how well these methods have performed on their data. The accessible style of the book ensures its readability for non-quantitative biologists. The data remain available, as benchmarks for future study, on the worldwide web.
Author: Joe Perry
Publisher: Springer Science & Business Media
ISBN: 9780412796906
Category: Mathematics
Page: 225
View: 6106
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
Author: Eckehard Schöll
Publisher: Cambridge University Press
ISBN: 0521451868
Category: Mathematics
Page: 406
View: 4752
Nonlinear Dynamics in Circuits
Author: Thomas L. Carroll,Louis M. Pecora
Publisher: World Scientific
ISBN: 9789810224387
Category: Science
Page: 336
View: 3167
Stability, Instability and Chaos
An Introduction to the Theory of Nonlinear Differential Equations
Author: Paul Glendinning
Publisher: Cambridge University Press
ISBN: 9780521425667
Category: Mathematics
Page: 388
View: 5991
An introduction to nonlinear differential equations which equips undergraduate students with the know-how to appreciate stability theory and bifurcation.
Author: Paul Glendinning
Publisher: Cambridge University Press
ISBN: 9780521425667
Category: Mathematics
Page: 388
View: 5991
Nonlinear Dynamics and Chaos
Author: J. M. T. Thompson,H. B. Stewart
Publisher: John Wiley & Sons
ISBN: 9780471876847
Category: Mathematics
Page: 437
View: 6312
Dynamical Systems in Neuroscience
Author: Eugene M. Izhikevich
Publisher: MIT Press
ISBN: 0262090430
Category: Medical
Page: 441
View: 7462