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Autor Yu, Pei |
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Título : Absolute Stability of Nonlinear Control Systems Tipo de documento: documento electrónico Autores: Liao, Xiaoxin ; SpringerLink (Online service) ; Yu, Pei Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2008 Colección: Mathematical Modelling: Theory and Applications, ISSN 1386-2960 num. 25 Número de páginas: XII, 384 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-8482-9 Idioma : Inglés (eng) Palabras clave: Mathematics Differential equations Applied mathematics Engineering System theory Vibration Dynamical systems Dynamics Ordinary Equations Systems Theory, Control Vibration, Systems, Applications of Clasificación: 51 Matemáticas Resumen: Following the recent developments in the field of absolute stability, Professor Xiaoxin Liao, in conjunction with Professor Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and the Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This includes nonlinear control systems with multiple controls, interval control systems, time-delay and neutral Lurie control systems, systems described by functional differential equations, the absolute stability for neural networks, as well as applications to chaos control and chaos synchronization. This book is aimed at undergraduates and lecturers in the areas of applied mathematics, nonlinear control systems and chaos control and synchronisation, but may also be useful as a reference work for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is required to gain a complete understanding of the workings and methodologies discussed within Nota de contenido: Principal Theorems on Global Stability -- Sufficient Conditions of Absolute Stability: Classical Methods -- Necessary and Sufficient Conditions for Absolute Stability -- Special Lurie-Type Control Systems -- Nonautonomous Systems -- Systems with Multiple Nonlinear Feedback Controls -- Robust Absolute Stability of Interval Control Systems -- Discrete Control Systems -- Time-Delayed and Neutral Lurie Control Systems -- Control Systems Described by Functional Differential Equations -- Absolute Stability of Hopfield Neural Network -- Application to Chaos Control and Chaos Synchronization En línea: http://dx.doi.org/10.1007/978-1-4020-8482-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34293 Absolute Stability of Nonlinear Control Systems [documento electrónico] / Liao, Xiaoxin ; SpringerLink (Online service) ; Yu, Pei . - Dordrecht : Springer Netherlands, 2008 . - XII, 384 p : online resource. - (Mathematical Modelling: Theory and Applications, ISSN 1386-2960; 25) .
ISBN : 978-1-4020-8482-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Differential equations Applied mathematics Engineering System theory Vibration Dynamical systems Dynamics Ordinary Equations Systems Theory, Control Vibration, Systems, Applications of Clasificación: 51 Matemáticas Resumen: Following the recent developments in the field of absolute stability, Professor Xiaoxin Liao, in conjunction with Professor Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and the Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This includes nonlinear control systems with multiple controls, interval control systems, time-delay and neutral Lurie control systems, systems described by functional differential equations, the absolute stability for neural networks, as well as applications to chaos control and chaos synchronization. This book is aimed at undergraduates and lecturers in the areas of applied mathematics, nonlinear control systems and chaos control and synchronisation, but may also be useful as a reference work for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is required to gain a complete understanding of the workings and methodologies discussed within Nota de contenido: Principal Theorems on Global Stability -- Sufficient Conditions of Absolute Stability: Classical Methods -- Necessary and Sufficient Conditions for Absolute Stability -- Special Lurie-Type Control Systems -- Nonautonomous Systems -- Systems with Multiple Nonlinear Feedback Controls -- Robust Absolute Stability of Interval Control Systems -- Discrete Control Systems -- Time-Delayed and Neutral Lurie Control Systems -- Control Systems Described by Functional Differential Equations -- Absolute Stability of Hopfield Neural Network -- Application to Chaos Control and Chaos Synchronization En línea: http://dx.doi.org/10.1007/978-1-4020-8482-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34293 Ejemplares
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Título : Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles Tipo de documento: documento electrónico Autores: Han, Maoan ; SpringerLink (Online service) ; Yu, Pei Editorial: London : Springer London Fecha de publicación: 2012 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 181 Número de páginas: XII, 404 p Il.: online resource ISBN/ISSN/DL: 978-1-4471-2918-9 Idioma : Inglés (eng) Palabras clave: Mathematics Approximation theory Dynamics Ergodic Differential equations Computer software Statistical physics Dynamical Systems and Theory Approximations Expansions Ordinary Equations Mathematical Software Nonlinear Clasificación: 51 Matemáticas Resumen: Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior Nota de contenido: Hopf Bifurcation and Normal Form Computation -- Comparison of Methods for Computing Focus Values -- Application (I)—Hilbert’s 16th Problem -- Application (II)—Practical Problems -- Fundamental Theory of the Melnikov Function Method -- Limit Cycle Bifurcations Near a Center -- Limit Cycles Near a Homoclinic or Heteroclinic Loop -- Finding More Limit Cycles Using Melnikov Functions -- Limit Cycle Bifurcations in Equivariant Systems En línea: http://dx.doi.org/10.1007/978-1-4471-2918-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32723 Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles [documento electrónico] / Han, Maoan ; SpringerLink (Online service) ; Yu, Pei . - London : Springer London, 2012 . - XII, 404 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 181) .
ISBN : 978-1-4471-2918-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Approximation theory Dynamics Ergodic Differential equations Computer software Statistical physics Dynamical Systems and Theory Approximations Expansions Ordinary Equations Mathematical Software Nonlinear Clasificación: 51 Matemáticas Resumen: Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior Nota de contenido: Hopf Bifurcation and Normal Form Computation -- Comparison of Methods for Computing Focus Values -- Application (I)—Hilbert’s 16th Problem -- Application (II)—Practical Problems -- Fundamental Theory of the Melnikov Function Method -- Limit Cycle Bifurcations Near a Center -- Limit Cycles Near a Homoclinic or Heteroclinic Loop -- Finding More Limit Cycles Using Melnikov Functions -- Limit Cycle Bifurcations in Equivariant Systems En línea: http://dx.doi.org/10.1007/978-1-4471-2918-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32723 Ejemplares
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