Two-dimensional Crossing-Variable Cubic Nonlinear Systems
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Product details:
- Edition number 2024
- Publisher Springer
- Date of Publication 12 February 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031628092
- Binding Hardback
- No. of pages386 pages
- Size 235x155 mm
- Language English
- Illustrations 1 Illustrations, black & white; 32 Illustrations, color 687
Categories
Short description:
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.
Long description:
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
More
Table of Contents:
Constant and crossing-cubic vector fields.- Crossing-linear and crossing-cubic vector fields.- Crossing-quadratic and crossing-cubic Vector Field.- Two crossing-cubic vector fields.
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