Polynomial functional dynamical systems / Albert C. J. Luo.
- 作者： Luo, Albert C. J., author.
- 其他題名：
- Synthesis lectures on mechanical engineering ;
- 出版： [San Rafael, California] : Morgan & Claypool Publishers 2022.
- 叢書名： Synthesis lectures on mechanical engineering,lecture #38
- 主題： Bifurcation theory. , Stability. , Dynamics. , Polynomials. , stability. , Bifurcation theory. , Dynamics. , Polynomials. , Stability.
- ISBN： 9781636392196 (pbk.) :: NT$1831 、 1636392199 (pbk.) 、 1636392210 (hbk.) 、 9781636392219 (hbk.)
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讀者標籤：
- 系統號： 005176338 | 機讀編目格式
館藏資訊
摘要註
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.