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1-dimensional flow arrays and bifurcations in planar polynomial systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	1-dimensional flow arrays and bifurcations in planar polynomial systemsby Albert C. J. Luo.
Author:	Luo, Albert C. J.
Published:	Singapore :Springer Nature Singapore :2024.
Description:	vii, 377 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Polynomials.
Online resource:	https://doi.org/10.1007/978-981-97-2204-4
ISBN:	9789819722044$q(electronic bk.)

1-dimensional flow arrays and bifurcations in planar polynomial systems
Luo, Albert C. J.

1-dimensional flow arrays and bifurcations in planar polynomial systems[electronic resource] /by Albert C. J. Luo. - Singapore :Springer Nature Singapore :2024. - vii, 377 p. :ill., digital ;24 cm.

Constant and Self variable Polynomial Systems -- Constant and Crossing variable Polynomial Systems -- Single univariate Polynomial Systems -- Higher order Infinite equilibrium Bifurcations.

This book introduces to 1-dimensional flow arrays and bifurcations in planar polynomial systems. The 1-dimensional source, sink and saddle flows are discussed, as well as the 1-dimensional parabola and inflection flows. The singular source, sink and saddle flows are the appearing and switching bifurcations for simple sink and source flow arrays and for lower-order singular source, sink and saddle flow arrays. The singular parabola and inflection flows are the appearing and switching bifurcations for simple parabola arrays and also for lower-order singular parabola and inflection flow arrays. The infinite-equilibriums in single-variable polynomial systems are also discussed, which are the appearing and switching bifurcations of hybrid arrays of source, sink, and saddle flows with parabola and inflections. This book helps readers understand the global dynamics of planar polynomial systems and the Hilbert sixteen problem.

ISBN: 9789819722044$q(electronic bk.)

Standard No.: 10.1007/978-981-97-2204-4doiSubjects--Topical Terms:

184760
Polynomials.

LC Class. No.: QA161.P59 / L86 2024

Dewey Class. No.: 512.9422

1-dimensional flow arrays and bifurcations in planar polynomial systems
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505 0 $a Constant and Self variable Polynomial Systems -- Constant and Crossing variable Polynomial Systems -- Single univariate Polynomial Systems -- Higher order Infinite equilibrium Bifurcations.
520 $a This book introduces to 1-dimensional flow arrays and bifurcations in planar polynomial systems. The 1-dimensional source, sink and saddle flows are discussed, as well as the 1-dimensional parabola and inflection flows. The singular source, sink and saddle flows are the appearing and switching bifurcations for simple sink and source flow arrays and for lower-order singular source, sink and saddle flow arrays. The singular parabola and inflection flows are the appearing and switching bifurcations for simple parabola arrays and also for lower-order singular parabola and inflection flow arrays. The infinite-equilibriums in single-variable polynomial systems are also discussed, which are the appearing and switching bifurcations of hybrid arrays of source, sink, and saddle flows with parabola and inflections. This book helps readers understand the global dynamics of planar polynomial systems and the Hilbert sixteen problem.
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