Polynomial Functional Dynamical Systems
暫譯: 多項式函數動態系統
Luo, Albert C. J.
- 出版商: Morgan & Claypool
- 出版日期: 2021-09-10
- 售價: $2,890
- 貴賓價: 9.5 折 $2,746
- 語言: 英文
- 頁數: 165
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1636392210
- ISBN-13: 9781636392219
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商品描述
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 are presented 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.
商品描述(中文翻譯)
這本書探討了多項式函數系統中平衡點的全球穩定性和分岔。書中討論了多項式函數系統中簡單和平衡點的高階分岔的出現和切換,這些平衡點的分岔不僅限於簡單平衡點,還包括高階平衡點。書中呈現了多項式函數系統中簡單平衡點的三階吸引子和源的分岔。此外,還介紹了鞍點和節點的三階吸引子和源的切換分岔,並針對兩個二階上鞍點和兩個二階下鞍點分別呈現了四階上鞍和下鞍的切換及出現分岔。一般而言,書中還介紹了(2k + 1)階的吸引子和源的切換分岔,針對(2k)階的鞍點和(2k + 1)階的節點,並針對(2k)階的上鞍和下鞍呈現了切換及出現的分岔,這些鞍點的階數為(2k)和(2k)(k = 1, 2, ...)。非線性動態系統中的向量場是多項式函數的。可以利用多項式代數結構構建複雜的動態系統,並且相應的奇異性和運動複雜性可以輕易地確定。