Polynomial Functional Dynamical Systems
Seiten
2021
Morgan & Claypool Publishers (Verlag)
978-1-63639-219-6 (ISBN)
Morgan & Claypool Publishers (Verlag)
978-1-63639-219-6 (ISBN)
Explores 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. Such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums.
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 (2𝑙 + 1)th-order sink and source switching bifurcations for (2𝑙𝑖)th-order saddles and (2𝑙𝑗 +1)-order nodes are also presented, and the (2𝑙)th-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for (2𝑙𝑖)th-order upper-saddles and (2𝑙𝑗)th-order lower-saddles (𝑖, 𝑗 = 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.
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 (2𝑙 + 1)th-order sink and source switching bifurcations for (2𝑙𝑖)th-order saddles and (2𝑙𝑗 +1)-order nodes are also presented, and the (2𝑙)th-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for (2𝑙𝑖)th-order upper-saddles and (2𝑙𝑗)th-order lower-saddles (𝑖, 𝑗 = 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.
Preface
Linear Functional Systems
Quadratic Nonlinear Functional Systems
Cubic Nonlinear Functional Systems
Quartic Nonlinear Functional Systems
(2𝑚)th-Degree Polynomial Functional Systems
(2𝑚+1)th-Degree Polynomial Functional Systems
Author's Biography
| Erscheinungsdatum | 15.09.2021 |
|---|---|
| Reihe/Serie | Synthesis Lectures on Mechanical Engineering |
| Verlagsort | San Rafael |
| Sprache | englisch |
| Maße | 191 x 235 mm |
| Gewicht | 333 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Technik ► Maschinenbau | |
| ISBN-10 | 1-63639-219-9 / 1636392199 |
| ISBN-13 | 978-1-63639-219-6 / 9781636392196 |
| Zustand | Neuware |
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Buch | Softcover (2022)
Springer Spektrum (Verlag)
CHF 55,95
