Two Dimensional Crossing Variable Cubic Nonlinear Systems
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Two Dimensional Crossing Variable Cubic Nonlinear Systems
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2024
Two Dimensional Crossing Variable Cubic Nonlinear Systems written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Equations, Cubic categories.
This book is the fourth of 15 related monographs presents systematically a theory of crossing-cubic nonlinear systems. In this treatment, at least one vector field is crossing-cubic, and the other vector field can be constant, crossing-linear, crossing-quadratic, and crossing-cubic. For constant vector fields, the dynamical systems possess 1-dimensional flows, such as parabola and inflection flows plus third-order parabola flows. For crossing-linear and crossing-cubic systems, the dynamical systems possess saddle and center equilibriums, parabola-saddles, third-order centers and saddles (i.e, (3rd UP+:UP+)-saddle and (3rdUP-:UP-)-saddle) and third-order centers (i.e., (3rd DP+:DP-)-center, (3rd DP-, DP+)-center) . For crossing-quadratic and crossing-cubic systems, in addition to the first and third-order saddles and centers plus parabola-saddles, there are (3:2)parabola-saddle and double-inflection saddles, and for the two crossing-cubic systems, (3:3)-saddles and centers exist. Finally, the homoclinic orbits with centers can be formed, and the corresponding homoclinic networks of centers and saddles exist. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations Develops equilibrium singularity and bifurcations in 2-dimensional self-cubic systems; Presents (1,3) and (3,3)-sink, source, and saddles; (1,2) and (3,2)-saddle-sink and saddle-source; (2,2)-double-saddles; Develops homoclinic networks of source, sink and saddles.
Two Dimensional Single Variable Cubic Nonlinear Systems Vol I
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2024-10-30
Two Dimensional Single Variable Cubic Nonlinear Systems Vol I written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-30 with Mathematics categories.
This book is the first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows.
Two Dimensional Single Variable Cubic Nonlinear Systems Vol Ii
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2024-11-19
Two Dimensional Single Variable Cubic Nonlinear Systems Vol Ii written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-19 with Science categories.
This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows. The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations
Two Dimensional Product Cubic Systems Vol I
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2024-10-31
Two Dimensional Product Cubic Systems Vol I written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-31 with Science categories.
This book, the fifth of 15 related monographs, presents systematically a theory of product-cubic nonlinear systems with constant and single-variable linear vector fields. The product-cubic vector field is a product of linear and quadratic different univariate functions. The hyperbolic and hyperbolic-secant flows with directrix flows in the cubic product system with a constant vector field are discussed first, and the cubic product systems with self-linear and crossing-linear vector fields are discussed. The inflection-source (sink) infinite equilibriums are presented for the switching bifurcations of a connected hyperbolic flow and saddle with hyperbolic-secant flow and source (sink) for the connected the separated hyperbolic and hyperbolic-secant flows. The inflection-sink and source infinite-equilibriums with parabola-saddles are presented for the switching bifurcations of a separated hyperbolic flow and saddle with a hyperbolic-secant flow and center. Readers learn new concepts, theory, phenomena, and analysis techniques, such as Constant and product-cubic systems, Linear-univariate and product-cubic systems, Hyperbolic and hyperbolic-secant flows, Connected hyperbolic and hyperbolic-secant flows, Separated hyperbolic and hyperbolic-secant flows, Inflection-source (sink) Infinite-equilibriums and Infinite-equilibrium switching bifurcations.
Limit Cycles And Homoclinic Networks In Two Dimensional Polynomial Systems
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2025-04-17
Limit Cycles And Homoclinic Networks In Two Dimensional Polynomial Systems written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-17 with Mathematics categories.
This book is a monograph about limit cycles and homoclinic networks in polynomial systems. The study of dynamical behaviors of polynomial dynamical systems was stimulated by Hilbert’s sixteenth problem in 1900. Many scientists have tried to work on Hilbert's sixteenth problem, but no significant results have been achieved yet. In this book, the properties of equilibriums in planar polynomial dynamical systems are studied. The corresponding first integral manifolds are determined. The homoclinic networks of saddles and centers (or limit cycles) in crossing-univariate polynomial systems are discussed, and the corresponding bifurcation theory is developed. The corresponding first integral manifolds are polynomial functions. The maximum numbers of centers and saddles in homoclinic networks are obtained, and the maximum numbers of sinks, sources, and saddles in homoclinic networks without centers are obtained as well. Such studies are to achieve global dynamics of planar polynomial dynamical systems, which can help one study global behaviors in nonlinear dynamical systems in physics, chemical reaction dynamics, engineering dynamics, and so on. This book is a reference for graduate students and researchers in the field of dynamical systems and control in mathematics, mechanical, and electrical engineering.
Mathematics As A Laboratory Tool
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Author : John Milton
language : en
Publisher: Springer
Release Date : 2014-09-18
Mathematics As A Laboratory Tool written by John Milton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-18 with Mathematics categories.
This introductory textbook is based on the premise that the foundation of good science is good data. The educational challenge addressed by this introductory textbook is how to present a sampling of the wide range of mathematical tools available for laboratory research to well-motivated students with a mathematical background limited to an introductory course in calculus.
A Modern Introduction To The Mathematical Theory Of Water Waves
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Author : Robin Stanley Johnson
language : en
Publisher: Cambridge University Press
Release Date : 1997-10-28
A Modern Introduction To The Mathematical Theory Of Water Waves written by Robin Stanley Johnson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-28 with Mathematics categories.
This text considers classical and modern problems in linear and non-linear water-wave theory.
Vibrations
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Author : Balakumar Balachandran
language : en
Publisher: Cambridge University Press
Release Date : 2018-11
Vibrations written by Balakumar Balachandran and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11 with Mathematics categories.
Provides an introduction to the modeling, analysis, design, measurement and real-world applications of vibrations, with online interactive graphics.
High Performance Computing In Biomedical Research
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Author : Theo C. Pilkington
language : en
Publisher: CRC Press
Release Date : 2020-09-10
High Performance Computing In Biomedical Research written by Theo C. Pilkington and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-10 with Science categories.
Leading researchers have contributed state-of-the-art chapters to this overview of high-performance computing in biomedical research. The book includes over 30 pages of color illustrations. Some of the important topics featured in the book include the following:
Metamaterial Analysis And Design
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Author : Habib Ammari
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-11-06
Metamaterial Analysis And Design written by Habib Ammari and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-06 with Mathematics categories.
Metamaterials are advanced composite materials which have exotic and powerful properties. Their complicated microstructures make metamaterials challenging to model, requiring the use of sophisticated mathematical techniques. This book uses a from-first-principles approach (based on boundary integral methods and asymptotic analysis) to study a class of high-contrast metamaterials. These mathematical techniques are applied to the problem of designing graded metamaterials that replicate the function of the cochlea.