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Two-dimensional self-independent variable cubic nonlinear systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Two-dimensional self-independent variable cubic nonlinear systemsby Albert C. J. Luo.
Author:	Luo, Albert C. J.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	x, 275 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Nonlinear systems.
Online resource:	https://doi.org/10.1007/978-3-031-57112-1
ISBN:	9783031571121$q(electronic bk.)

Two-dimensional self-independent variable cubic nonlinear systems
Luo, Albert C. J.

Two-dimensional self-independent variable cubic nonlinear systems[electronic resource] /by Albert C. J. Luo. - Cham :Springer Nature Switzerland :2024. - x, 275 p. :ill. (chiefly color), digital ;24 cm.

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.

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 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.

ISBN: 9783031571121$q(electronic bk.)

Standard No.: 10.1007/978-3-031-57112-1doiSubjects--Topical Terms:

182906
Nonlinear systems.

LC Class. No.: QA613.619

Dewey Class. No.: 515.63

Two-dimensional self-independent variable cubic nonlinear systems
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245 1 0 $a Two-dimensional self-independent variable cubic nonlinear systems $h [electronic resource] / $c by Albert C. J. Luo.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a x, 275 p. : $b ill. (chiefly color), digital ; $c 24 cm.
505 0 $a 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.
520 $a 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 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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650 1 4 $a Waves, instabilities and nonlinear plasma dynamics. $3 919553
650 2 4 $a Applied Dynamical Systems. $3 913436
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