Polynomial functional dynamical systems / Albert C. J. Luo.

Format:

Book

Author/Creator:

Luo, Albert C. J., author.

Series:

Synthesis lectures on mechanical engineering.

Synthesis lectures on mechanical engineering

Language:

English

Subjects (All):

Bifurcation theory.

Physical Description:

1 online resource (159 pages).

Place of Publication:

[Place of publication not identified] : Springer, 2022.

Summary:

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.

Notes:

Description based on print version record.

ISBN:

9783031797095

3031797094