A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.
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Editorial Reviews
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"This is a volume in the series Cambridge Texts in Applied mathematics. It is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as the parameter varies..." Quarterly of Applied Mathematics
"...can be used as an effective text to introduce the topics involved with nonlinear dynamics." Subhash C. Sinha, Applied Mechanics Review
"...a useful book which contains an abundance of interesting problems and so will be of immense value to anyone planning a course on the subject." Tom Mullin, The Times Higher Education Supplement
"...we have not yet seen in the literature any generally accepted textbooks...It seems to me that this book is an honest and praiseworthy attempt to fill precisely this educational gap. In my opinion, it is quite successful in this regard, and its aim to attract and stimulate the curious student of applied sciences is largely fulfilled....well-written and well equipped to serve as a text, from which teachers and students will find much to draw upon in order to improve their working knowledge of nonlinear dynamics and chaos....I highly recommend it." Tassos Bountis, Mathematical Reviews
"The strength of this book lies in its examples and exercises. Each topic is illustrated with marvelously detailed examples, and there is a total of 214 exercises with many solutions and hints." Joseph Gruendler, SIAM Review
"...can be used as an effective text to introduce the topics involved with nonlinear dynamics." Subhash C. Sinha, Applied Mechanics Review
"...a useful book which contains an abundance of interesting problems and so will be of immense value to anyone planning a course on the subject." Tom Mullin, The Times Higher Education Supplement
"...we have not yet seen in the literature any generally accepted textbooks...It seems to me that this book is an honest and praiseworthy attempt to fill precisely this educational gap. In my opinion, it is quite successful in this regard, and its aim to attract and stimulate the curious student of applied sciences is largely fulfilled....well-written and well equipped to serve as a text, from which teachers and students will find much to draw upon in order to improve their working knowledge of nonlinear dynamics and chaos....I highly recommend it." Tassos Bountis, Mathematical Reviews
"The strength of this book lies in its examples and exercises. Each topic is illustrated with marvelously detailed examples, and there is a total of 214 exercises with many solutions and hints." Joseph Gruendler, SIAM Review
Book Description
The text introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. Worked examples and problems are used to motivate and illustrate the general principles.
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2 of 4 people found the following review helpful:
5.0 out of 5 stars
Examples and problems work well with MathCad,
By pyramidl@trilobyte.net (Tooele, Ut.) - See all my reviews
This review is from: Nonlinear Systems (Cambridge Texts in Applied Mathematics) (Paperback)
Book offers an over view of the problem, without becoming bogged in "favorite" topics. Integration of soln. with Mathcad and actual simulations are relatively easy. Description of z^2 plane fractals as an exception (also the start of fractals in more complex systems)is worth price of book alone. Drazin's "outline" for the analysis of non-linear systems is a pure bonus.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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sawtooth map, sketch the bifurcation diagram, neighbouring orbits, weakly nonlinear oscillations, null solution, simple turning point, transcritical bifurcation, flip bifurcation, supercritical pitchfork bifurcation, logistic difference equation, weakly nonlinear theory, sketch the phase portrait, unsteady solutions, homoclinic orbit, negative stiffness, linearized system, show that the origin, ordinary differential systems, bifurcation curves, bifurcation set, manifolds intersect, logistic map, topological character, chaotic solutions, period doubling New!
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sawtooth map, sketch the bifurcation diagram, neighbouring orbits, weakly nonlinear oscillations, null solution, simple turning point, transcritical bifurcation, flip bifurcation, supercritical pitchfork bifurcation, logistic difference equation, weakly nonlinear theory, sketch the phase portrait, unsteady solutions, homoclinic orbit, negative stiffness, linearized system, show that the origin, ordinary differential systems, bifurcation curves, bifurcation set, manifolds intersect, logistic map, topological character, chaotic solutions, period doubling New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 40
books:
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100
books
cite this book:
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- Ordinary Differential Equations (Modular Mathematics Series) by William Cox in Back Matter
- Time Series Analysis by M . B . Priestley in Back Matter
- Statistical Physics, Third Edition, Part 1: Volume 5 (Course of Theoretical Physics, Volume 5) by L D Landau in Back Matter
- Iterated Maps on the Interval as Dynamical System by Pierre Collet in Back Matter
- Qualitative Theory of Differential Equations (Dover Books on Mathematics) by V. V. Nemytskii in Back Matter
See all 40 books this book cites
- Introduction to Hydrodynamic Stability (Cambridge Texts in Applied Mathematics) by P. G. Drazin in Front Matter, and Back Matter
- Lagrangian and Hamiltonian Methods for Nonlinear Control 2000: A Proceedings volume from the IFAC Workshop, Princeton, New Jersey, USA, 16 - 18 March 2000 (IFAC Proceedings Volumes) by N.E. Leonard on page 37, and page 80
- Remapping Reality: Chaos and Creativity in Science and Literature (Goethe - Nietzsche - Grass) (Internationale Forschungen zur Allgemeinen und ... & Vergleichenden Literaturwissenschaft) by John A. McCarthy on page 100, and Back Matter
- An Introduction to Numerical Analysis by Endre Süli on page 34, and Back Matter
- New Directions and Applications in Control Theory (Lecture Notes in Control and Information Sciences) by Wijesuriya P. Dayawansa on page 181, and page 305
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