Methods Of Qualitative Theory In Nonlinear Dynamics (Part I)

Methods Of Qualitative Theory In Nonlinear Dynamics (Part I)

Author: Leonid P Shilnikov

Publisher: World Scientific

Published: 1998-12-08

Total Pages: 418

ISBN-13: 9814496421

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Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form.In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.


Book Synopsis Methods Of Qualitative Theory In Nonlinear Dynamics (Part I) by : Leonid P Shilnikov

Download or read book Methods Of Qualitative Theory In Nonlinear Dynamics (Part I) written by Leonid P Shilnikov and published by World Scientific. This book was released on 1998-12-08 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form.In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.

Methods of Qualitative Theory in Nonlinear Dynamics

Methods of Qualitative Theory in Nonlinear Dynamics

Author: Leonid P. Shilnikov

Publisher: World Scientific

Published: 1998

Total Pages: 420

ISBN-13: 9789810233822

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Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.


Book Synopsis Methods of Qualitative Theory in Nonlinear Dynamics by : Leonid P. Shilnikov

Download or read book Methods of Qualitative Theory in Nonlinear Dynamics written by Leonid P. Shilnikov and published by World Scientific. This book was released on 1998 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.

Methods of Qualitative Theory in Nonlinear Dynamics

Methods of Qualitative Theory in Nonlinear Dynamics

Author: L. P. Shilʹnikov

Publisher:

Published: 1998

Total Pages: 957

ISBN-13: 9789810233822

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Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject


Book Synopsis Methods of Qualitative Theory in Nonlinear Dynamics by : L. P. Shilʹnikov

Download or read book Methods of Qualitative Theory in Nonlinear Dynamics written by L. P. Shilʹnikov and published by . This book was released on 1998 with total page 957 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject

Methods Of Qualitative Theory In Nonlinear Dynamics (Part Ii)

Methods Of Qualitative Theory In Nonlinear Dynamics (Part Ii)

Author: Leon O Chua

Publisher: World Scientific

Published: 2001-09-27

Total Pages: 591

ISBN-13: 9814494291

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Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form.In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.


Book Synopsis Methods Of Qualitative Theory In Nonlinear Dynamics (Part Ii) by : Leon O Chua

Download or read book Methods Of Qualitative Theory In Nonlinear Dynamics (Part Ii) written by Leon O Chua and published by World Scientific. This book was released on 2001-09-27 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form.In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.

Methods of Qualitative Theory in Nonlinear Dynamics

Methods of Qualitative Theory in Nonlinear Dynamics

Author: Leonid P. Shilnikov

Publisher:

Published: 2001

Total Pages:

ISBN-13:

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Book Synopsis Methods of Qualitative Theory in Nonlinear Dynamics by : Leonid P. Shilnikov

Download or read book Methods of Qualitative Theory in Nonlinear Dynamics written by Leonid P. Shilnikov and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Methods of Qualitative Theory in Nonlinear Dynamics

Methods of Qualitative Theory in Nonlinear Dynamics

Author: L. P. Shil'nikov

Publisher: World Scientific

Published: 2001

Total Pages: 591

ISBN-13: 9812798552

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Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need. Following the footsteps of Poincar(r), and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form. In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject. Sample Chapter(s). Introduction to Part II (124 KB). Chapter 7.1: Rough systems on a plane. Andronov-Pontryagin theorem (218 KB). Chapter 7.2: The set of center motions (158 KB). Chapter 7.3: General classification of center motions (155 KB). Chapter 7.4: Remarks on roughness of high-order dynamical systems (136 KB). Chapter 7.5: Morse-Smale systems (435 KB). Chapter 7.6: Some properties of Morse-Smale systems (211 KB). Contents: Structurally Stable Systems; Bifurcations of Dynamical Systems; The Behavior of Dynamical Systems on Stability Boundaries of Equilibrium States; The Behavior of Dynamical Systems on Stability Boundaries of Periodic Trajectories; Local Bifurcations on the Route Over Stability Boundaries; Global Bifurcations at the Disappearance of a Saddle-Node Equilibrium States and Periodic Orbits; Bifurcations of Homoclinic Loops of Saddle Equilibrium States; Safe and Dangerous Boundaries. Readership: Engineers, students, mathematicians and researchers in nonlinear dynamics and dynamical systems.


Book Synopsis Methods of Qualitative Theory in Nonlinear Dynamics by : L. P. Shil'nikov

Download or read book Methods of Qualitative Theory in Nonlinear Dynamics written by L. P. Shil'nikov and published by World Scientific. This book was released on 2001 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need. Following the footsteps of Poincar(r), and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in the book have been developed only recently and have not yet appeared in textbook form. In keeping with the self-contained nature of the book, all the topics are developed with introductory background and complete mathematical rigor. Generously illustrated and written at a high level of exposition, this invaluable book will appeal to both the beginner and the advanced student of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject. Sample Chapter(s). Introduction to Part II (124 KB). Chapter 7.1: Rough systems on a plane. Andronov-Pontryagin theorem (218 KB). Chapter 7.2: The set of center motions (158 KB). Chapter 7.3: General classification of center motions (155 KB). Chapter 7.4: Remarks on roughness of high-order dynamical systems (136 KB). Chapter 7.5: Morse-Smale systems (435 KB). Chapter 7.6: Some properties of Morse-Smale systems (211 KB). Contents: Structurally Stable Systems; Bifurcations of Dynamical Systems; The Behavior of Dynamical Systems on Stability Boundaries of Equilibrium States; The Behavior of Dynamical Systems on Stability Boundaries of Periodic Trajectories; Local Bifurcations on the Route Over Stability Boundaries; Global Bifurcations at the Disappearance of a Saddle-Node Equilibrium States and Periodic Orbits; Bifurcations of Homoclinic Loops of Saddle Equilibrium States; Safe and Dangerous Boundaries. Readership: Engineers, students, mathematicians and researchers in nonlinear dynamics and dynamical systems.

Methods of Qualitative Theory in Nonlinear Dynamics: Basic Concepts

Methods of Qualitative Theory in Nonlinear Dynamics: Basic Concepts

Author:

Publisher:

Published:

Total Pages: 0

ISBN-13:

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Book Synopsis Methods of Qualitative Theory in Nonlinear Dynamics: Basic Concepts by :

Download or read book Methods of Qualitative Theory in Nonlinear Dynamics: Basic Concepts written by and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Methods of Qualitative Theory in Nonlinear Dynamics: Structurally Stable Systems

Methods of Qualitative Theory in Nonlinear Dynamics: Structurally Stable Systems

Author:

Publisher:

Published:

Total Pages: 0

ISBN-13:

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Book Synopsis Methods of Qualitative Theory in Nonlinear Dynamics: Structurally Stable Systems by :

Download or read book Methods of Qualitative Theory in Nonlinear Dynamics: Structurally Stable Systems written by and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Qualitative Methods in Nonlinear Dynamics

Qualitative Methods in Nonlinear Dynamics

Author: A.A. Martynyuk

Publisher: CRC Press

Published: 2001-11-05

Total Pages: 326

ISBN-13: 9780824707354

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"Presents new approaches to qualitative analysis of continuous, discreteptime, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability."


Book Synopsis Qualitative Methods in Nonlinear Dynamics by : A.A. Martynyuk

Download or read book Qualitative Methods in Nonlinear Dynamics written by A.A. Martynyuk and published by CRC Press. This book was released on 2001-11-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Presents new approaches to qualitative analysis of continuous, discreteptime, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability."

Qualitative and Quantitative Analysis of Nonlinear Systems

Qualitative and Quantitative Analysis of Nonlinear Systems

Author: Michael Z. Zgurovsky

Publisher: Springer

Published: 2017-07-11

Total Pages: 240

ISBN-13: 3319598406

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Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and their approximations; (c) uniform global behavior of solutions in time; and (d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for the investigation of dissipative dynamical systems with several applications including nonlinear parabolic equations of divergent form, nonlinear stochastic equations of parabolic type, unilateral problems, nonlinear PDEs on Riemannian manifolds with or without boundary, contact problems as well as particular examples is established. As such, the book is addressed to a wide circle of mathematical, mechanical and engineering readers.


Book Synopsis Qualitative and Quantitative Analysis of Nonlinear Systems by : Michael Z. Zgurovsky

Download or read book Qualitative and Quantitative Analysis of Nonlinear Systems written by Michael Z. Zgurovsky and published by Springer. This book was released on 2017-07-11 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and their approximations; (c) uniform global behavior of solutions in time; and (d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for the investigation of dissipative dynamical systems with several applications including nonlinear parabolic equations of divergent form, nonlinear stochastic equations of parabolic type, unilateral problems, nonlinear PDEs on Riemannian manifolds with or without boundary, contact problems as well as particular examples is established. As such, the book is addressed to a wide circle of mathematical, mechanical and engineering readers.