Two-dimensional Self-independent Variable Cubic Nonlinear Systems
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Product details:
- Edition number 2024
- Publisher Springer
- Date of Publication 8 November 2024
- Number of Volumes 1 pieces, Book
- ISBN 9783031571114
- Binding Hardback
- No. of pages275 pages
- Size 235x155 mm
- Language English
- Illustrations 1 Illustrations, black & white; 32 Illustrations, color 661
Categories
Short description:
This book is the third of 15 related monographs, presents systematically a theory of self-cubic nonlinear systems. Here, at least one vector field is self-cubic, the other vector fields can be constant, self-linear, self-quadratic, and 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, the dynamical systems possess source, sink, and saddle equilibriums, saddle-source and saddle-sink equilibriums, third-order source and sink (i.e., ( 3rdSO:SO)-source, ( 3rdSI:SI)-sink) and third-order saddle (i.e., (3rdSO:SI)-saddle, 3rdSI:SO)-saddle). For self-quadratic and self-cubic systems, in addition to the first and third-order source, sink, saddles plus saddle-source, saddle-sink, there are (3,2)-saddle-sink, (3,2)-saddle-source and double-saddles, and for the two self-cubic systems, double third-order source, sink and saddles exist. Finally, the authors describes thar the homoclinic orbits without cen-ters can be formed, and the corresponding homoclinic networks of source, sink and saddles exist.
• 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.
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Long description:
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
Table of Contents:
Constant and Self-Cubic Vector fields.- Self-linear and Self-cubic vector fields.- Self-quadratic and self-cubic vector fields .- Two self-cubic vector fields.
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