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Polynomial Functional Dynamical Systems [electronic resource] / by Albert Luo.

By: Luo, Albert [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Mechanical Engineering: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2021Edition: 1st ed. 2021.Description: XIII, 151 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031797095.Subject(s): Engineering | Electrical engineering | Engineering design | Microtechnology | Microelectromechanical systems | Technology and Engineering | Electrical and Electronic Engineering | Engineering Design | Microsystems and MEMSAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 620 Online resources: Click here to access online
Contents:
Preface -- Linear Functional Systems -- Quadratic Nonlinear Functional Systems -- Cubic Nonlinear Functional Systems -- Quartic Nonlinear Functional Systems -- (2??)th-Degree Polynomial Functional Systems -- (2??+1)th-Degree Polynomial Functional Systems -- Author's Biography.
In: Springer Nature eBookSummary: The book is about the global stability and bifurcation of equilibriums in polynomial functional systems. Appearing and switching bifurcations of simple and higher-order equilibriums in the polynomial functional systems are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The third-order sink and source bifurcations for simple equilibriums are presented in the polynomial functional systems. The third-order sink and source switching bifurcations for saddle and nodes are also presented, and the fourth-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for two second-order upper-saddles and two second-order lower-saddles, respectively. In general, the (2���� + 1)th-order sink and source switching bifurcations for (2��������)th-order saddles and (2�������� +1)-order nodes are also presented, and the (2����)th-order upper-saddle and lower-saddle switching and appearing bifurcations arepresented for (2��������)th-order upper-saddles and (2��������)th-order lower-saddles (����, ���� = 1,2,...). The vector fields in nonlinear dynamical systems are polynomial functional. Complex dynamical systems can be constructed with polynomial algebraic structures, and the corresponding singularity and motion complexity can be easily determined.
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Preface -- Linear Functional Systems -- Quadratic Nonlinear Functional Systems -- Cubic Nonlinear Functional Systems -- Quartic Nonlinear Functional Systems -- (2??)th-Degree Polynomial Functional Systems -- (2??+1)th-Degree Polynomial Functional Systems -- Author's Biography.

The book is about the global stability and bifurcation of equilibriums in polynomial functional systems. Appearing and switching bifurcations of simple and higher-order equilibriums in the polynomial functional systems are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The third-order sink and source bifurcations for simple equilibriums are presented in the polynomial functional systems. The third-order sink and source switching bifurcations for saddle and nodes are also presented, and the fourth-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for two second-order upper-saddles and two second-order lower-saddles, respectively. In general, the (2���� + 1)th-order sink and source switching bifurcations for (2��������)th-order saddles and (2�������� +1)-order nodes are also presented, and the (2����)th-order upper-saddle and lower-saddle switching and appearing bifurcations arepresented for (2��������)th-order upper-saddles and (2��������)th-order lower-saddles (����, ���� = 1,2,...). The vector fields in nonlinear dynamical systems are polynomial functional. Complex dynamical systems can be constructed with polynomial algebraic structures, and the corresponding singularity and motion complexity can be easily determined.

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