Nonlinear Systems and Their Remarkable Mathematical Structures

Nonlinear Systems and Their Remarkable Mathematical Structures

Author: Norbert Euler

Publisher: CRC Press

Published: 2019-12-06

Total Pages: 541

ISBN-13: 0429554303

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Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics


Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures by : Norbert Euler

Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures written by Norbert Euler and published by CRC Press. This book was released on 2019-12-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics

Nonlinear Systems and Their Remarkable Mathematical Structures Volume II

Nonlinear Systems and Their Remarkable Mathematical Structures Volume II

Author: Norbert Euler

Publisher: CRC Press

Published: 2019-11-19

Total Pages: 540

ISBN-13: 9780367208479

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Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics


Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures Volume II by : Norbert Euler

Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures Volume II written by Norbert Euler and published by CRC Press. This book was released on 2019-11-19 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics

Nonlinear Systems and Their Remarkable Mathematical Structures

Nonlinear Systems and Their Remarkable Mathematical Structures

Author: Taylor & Francis Group

Publisher: CRC Press

Published: 2020-12-18

Total Pages: 582

ISBN-13: 9780367732431

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Nonlinear Systems and Their Remarkable Mathematical Structures aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-expert in this field Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics Serves as a literature source in nonlinear systems


Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures by : Taylor & Francis Group

Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures written by Taylor & Francis Group and published by CRC Press. This book was released on 2020-12-18 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Systems and Their Remarkable Mathematical Structures aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-expert in this field Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics Serves as a literature source in nonlinear systems

Nonlinear Systems and Their Remarkable Mathematical Structures

Nonlinear Systems and Their Remarkable Mathematical Structures

Author: Norbert Euler

Publisher: CRC Press

Published: 2021-09-07

Total Pages: 367

ISBN-13: 1000423301

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The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained


Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures by : Norbert Euler

Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures written by Norbert Euler and published by CRC Press. This book was released on 2021-09-07 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained

Nonlinear Systems and Their Remarkable Mathematical Structures Volumes 1 2 And 3

Nonlinear Systems and Their Remarkable Mathematical Structures Volumes 1 2 And 3

Author: Taylor & Francis Group

Publisher:

Published: 2021-09-30

Total Pages:

ISBN-13: 9780367208547

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Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures Volumes 1 2 And 3 by : Taylor & Francis Group

Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures Volumes 1 2 And 3 written by Taylor & Francis Group and published by . This book was released on 2021-09-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Control Systems II

Nonlinear Control Systems II

Author: Alberto Isidori

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 300

ISBN-13: 1447105494

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This eagerly awaited follow-up to Nonlinear Control Systems incorporates recent advances in the design of feedback laws, for the purpose of globally stabilizing nonlinear systems via state or output feedback. The author is one of the most prominent researchers in the field.


Book Synopsis Nonlinear Control Systems II by : Alberto Isidori

Download or read book Nonlinear Control Systems II written by Alberto Isidori and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This eagerly awaited follow-up to Nonlinear Control Systems incorporates recent advances in the design of feedback laws, for the purpose of globally stabilizing nonlinear systems via state or output feedback. The author is one of the most prominent researchers in the field.

Nonlinear Systems

Nonlinear Systems

Author: P. G. Drazin

Publisher: Cambridge University Press

Published: 1992-06-26

Total Pages: 354

ISBN-13: 9780521406680

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The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limited to knowledge of linear algebra and advanced calculus, thus making it ideally suited to both senior undergraduates and postgraduates from physics, engineering, chemistry, meteorology etc. as well as mathematics.


Book Synopsis Nonlinear Systems by : P. G. Drazin

Download or read book Nonlinear Systems written by P. G. Drazin and published by Cambridge University Press. This book was released on 1992-06-26 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limited to knowledge of linear algebra and advanced calculus, thus making it ideally suited to both senior undergraduates and postgraduates from physics, engineering, chemistry, meteorology etc. as well as mathematics.

Continuous Symmetries and Integrability of Discrete Equations

Continuous Symmetries and Integrability of Discrete Equations

Author: Decio Levi

Publisher: American Mathematical Society, Centre de Recherches Mathématiques

Published: 2023-01-23

Total Pages: 520

ISBN-13: 0821843540

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This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.


Book Synopsis Continuous Symmetries and Integrability of Discrete Equations by : Decio Levi

Download or read book Continuous Symmetries and Integrability of Discrete Equations written by Decio Levi and published by American Mathematical Society, Centre de Recherches Mathématiques. This book was released on 2023-01-23 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.

Two-Dimensional Quadratic Nonlinear Systems

Two-Dimensional Quadratic Nonlinear Systems

Author: Albert C. J. Luo

Publisher: Springer Nature

Published: 2022-03-29

Total Pages: 453

ISBN-13: 9811678693

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The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering.


Book Synopsis Two-Dimensional Quadratic Nonlinear Systems by : Albert C. J. Luo

Download or read book Two-Dimensional Quadratic Nonlinear Systems written by Albert C. J. Luo and published by Springer Nature. This book was released on 2022-03-29 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering.

Two-Dimensional Quadratic Nonlinear Systems

Two-Dimensional Quadratic Nonlinear Systems

Author: Albert C. J. Luo

Publisher: Springer Nature

Published: 2023-04-19

Total Pages: 692

ISBN-13: 9811678731

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This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert’s sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering.


Book Synopsis Two-Dimensional Quadratic Nonlinear Systems by : Albert C. J. Luo

Download or read book Two-Dimensional Quadratic Nonlinear Systems written by Albert C. J. Luo and published by Springer Nature. This book was released on 2023-04-19 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert’s sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering.