Two Dimensional Single Variable Cubic Nonlinear Systems Vol I

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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 Self Independent Variable Cubic Nonlinear Systems

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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2024-11-07

Two Dimensional Self Independent 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 2024-11-07 with Science categories.

This book, the third of 15 related monographs, presents systematically a theory of self-independent cubic nonlinear systems. Here, at least one vector field is self-cubic, and the other vector field can be constant, self-linear, self-quadratic, or self-cubic. For constant vector fields in this book, the dynamical systems possess 1-dimensional flows, such as source, sink and saddle flows, plus third-order source and sink flows. For self-linear and self-cubic systems discussed, the dynamical systems possess source, sink and saddle equilibriums, saddle-source and saddle-sink, third-order sink and source (i.e, (3rd SI:SI)-sink and (3rdSO:SO)-source) and third-order source (i.e., (3rd SO:SI)-saddle, (3rd SI, SO)-saddle) . For self-quadratic and self-cubic systems, in addition to the first and third-order sink, source and saddles plus saddle-source and saddle-sink, there are (3:2)-saddle-sink and (3:2) saddle-source and double-saddles. For the two self-cubic systems, (3:3)-source, sink and saddles exist. Finally, the author describes that homoclinic orbits without centers can be formed, and the corresponding homoclinic networks of source, sink and saddles exists. 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

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.

Surveys In Applied Mathematics

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Author : Mark I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Surveys In Applied Mathematics written by Mark I. Freidlin 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.

Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.

Scattering Two Volume Set

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Author : E. R. Pike
language : en
Publisher: Elsevier
Release Date : 2001-10-09

Scattering Two Volume Set written by E. R. Pike and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-09 with Science categories.

Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium. Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering. This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research. The first interdisciplinary reference source on scattering to gather all world expertise in this technique Covers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplines The list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering

The Theory Of Chaotic Attractors

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Author : Brian R. Hunt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-05

The Theory Of Chaotic Attractors written by Brian R. Hunt 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 2013-06-05 with Mathematics categories.

The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting, outstanding papers for detailed study and comparison. We hope that this book will allow serious graduate students to hold seminars to study how the research in this field developed. Limitation of space forced us painfully to exclude many excellent, relevant papers, and the resulting choice reflects the interests of the editors. Since James Alan Yorke was born August 3, 1941, we chose to have this book commemorate his sixtieth birthday, honoring his research in this field. The editors are four of his collaborators. We would particularly like to thank Achi Dosanjh (senior editor math ematics), Elizabeth Young (assistant editor mathematics), Joel Ariaratnam (mathematics editorial), and Yong-Soon Hwang (book production editor) from Springer Verlag in New York for their efforts in publishing this book.

Japanese Science And Technology

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Author :
language : en
Publisher:
Release Date : 1986

Japanese Science And Technology written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.

Peregrine Soliton And Breathers In Wave Physics Achievements And Perspectives

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Author : Bertrand Kibler
language : en
Publisher: Frontiers Media SA
Release Date : 2022-08-16

Peregrine Soliton And Breathers In Wave Physics Achievements And Perspectives written by Bertrand Kibler and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-16 with Science categories.

Scientific And Technical Aerospace Reports

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Author :
language : en
Publisher:
Release Date : 1990

Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Aeronautics categories.