Non Linear Differential Equations And Dynamical Systems
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Nonlinear Differential Equations And Dynamical Systems
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Author : Feliz Manuel Minhós
language : en
Publisher: MDPI
Release Date : 2021-04-15
Nonlinear Differential Equations And Dynamical Systems written by Feliz Manuel Minhós and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Mathematics categories.
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Nonlinear Differential Equations And Dynamical Systems
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Differential Equations And Dynamical Systems written by Ferdinand Verhulst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises.
Non Linear Differential Equations And Dynamical Systems
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Author : Luis Manuel Braga da Costa Campos
language : en
Publisher: CRC Press
Release Date : 2019-11-05
Non Linear Differential Equations And Dynamical Systems written by Luis Manuel Braga da Costa Campos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Mathematics categories.
Non-Linear Differential Equations and Dynamical Systems is the second book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This second book consists of two chapters (chapters 3 and 4 of the set). The first chapter considers non-linear differential equations of first order, including variable coefficients. A first-order differential equation is equivalent to a first-order differential in two variables. The differentials of order higher than the first and with more than two variables are also considered. The applications include the representation of vector fields by potentials. The second chapter in the book starts with linear oscillators with coefficients varying with time, including parametric resonance. It proceeds to non-linear oscillators including non-linear resonance, amplitude jumps, and hysteresis. The non-linear restoring and friction forces also apply to electromechanical dynamos. These are examples of dynamical systems with bifurcations that may lead to chaotic motions. Presents general first-order differential equations including non-linear like the Ricatti equation Discusses differentials of the first or higher order in two or more variables Includes discretization of differential equations as finite difference equations Describes parametric resonance of linear time dependent oscillators specified by the Mathieu functions and other methods Examines non-linear oscillations and damping of dynamical systems including bifurcations and chaotic motions
Nonlinear Differential Equations And Dynamical Systems
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Author : Feliz Manuel Minhós
language : en
Publisher:
Release Date : 2021
Nonlinear Differential Equations And Dynamical Systems written by Feliz Manuel Minhós and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties' oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator-prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Differential Equations And Dynamical Systems
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Author : Lawrence Perko
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-01
Differential Equations And Dynamical Systems written by Lawrence Perko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-01 with Mathematics categories.
This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.
Nonlinear Ordinary Differential Equations
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Author : Dominic William Jordan
language : en
Publisher: Oxford University Press, USA
Release Date : 1999
Nonlinear Ordinary Differential Equations written by Dominic William Jordan and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos.
Differential Equations Dynamical Systems And An Introduction To Chaos
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Author : Morris W. Hirsch
language : en
Publisher: Academic Press
Release Date : 2004
Differential Equations Dynamical Systems And An Introduction To Chaos written by Morris W. Hirsch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Business & Economics categories.
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.
Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations
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Author : Tong-ren Ding
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-08-13
Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations written by Tong-ren Ding and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems. Elementary knowledge is emphasized by the detailed discussions on the fundamental theorems of the Cauchy problem, fixed-point theorems (especially the twist theorems), the principal idea of dynamical systems, the nonlinear oscillation of Duffing's equation, and some special analyses of particular differential equations. It also contains the latest research by the author as an integral part of the book.
Differential Equations Dynamical Systems And Linear Algebra
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Author : Morris W. Hirsch
language : en
Publisher: Academic Press
Release Date : 1974-06-28
Differential Equations Dynamical Systems And Linear Algebra written by Morris W. Hirsch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-06-28 with Mathematics categories.
This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.
Fundamentals Of Ordinary Differential Equations
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Author : Mohit Chatterjee
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Fundamentals Of Ordinary Differential Equations written by Mohit Chatterjee and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Fundamentals of Ordinary Differential Equations" is a comprehensive guide designed for students, researchers, and professionals to master ODE theory and applications. We cover essential principles, advanced techniques, and practical applications, providing a well-rounded resource for understanding differential equations and their real-world impact. The book offers a multifaceted approach, from basic principles to advanced concepts, catering to fields like physics, engineering, biology, and economics. Mathematical ideas are broken down with step-by-step explanations, examples, and illustrations, making complex concepts accessible. Real-world examples throughout each chapter show how ODEs model and analyze systems in diverse disciplines. We also explain numerical methods such as Euler’s method, Runge-Kutta, and finite differences, equipping readers with computational tools for solving ODEs. Advanced topics include bifurcation, chaos theory, Hamiltonian systems, and singular perturbations, providing an in-depth grasp of ODE topics. With chapter summaries, exercises, glossaries, and additional resources, "Fundamentals of Ordinary Differential Equations" is an essential reference for students, professionals, and practitioners across science and engineering fields.