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Polynomial Functional Dynamical Systemsnalbert C J Luo Southern Illinois University Edwardsville
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Book Synopsis Polynomial Functional Dynamical Systems$nAlbert C. J. Luo (Southern Illinois University, Edwardsville). by : Albert C. J. Luo
Download or read book Polynomial Functional Dynamical Systems$nAlbert C. J. Luo (Southern Illinois University, Edwardsville). written by Albert C. J. Luo and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Polynomial Functional Dynamical Systems by : Albert C. J. Luo
Download or read book Polynomial Functional Dynamical Systems written by Albert C. J. Luo and published by Morgan & Claypool Publishers. This book was released on 2021-09-10 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Limit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems by : Albert C. J. Luo
Download or read book Limit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems written by Albert C. J. Luo and published by Springer. This book was released on 2024-10-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a monograph about limit cycles and homoclinic networks in polynomial systems. The study of dynamical behaviors of polynomial dynamical systems was stimulated by Hilbert’s sixteenth problem in 1900. Many scientists have tried to work on Hilbert's sixteenth problem, but no significant results have been achieved yet. In this book, the properties of equilibriums in planar polynomial dynamical systems are studied. The corresponding first integral manifolds are determined. The homoclinic networks of saddles and centers (or limit cycles) in crossing-univariate polynomial systems are discussed, and the corresponding bifurcation theory is developed. The corresponding first integral manifolds are polynomial functions. The maximum numbers of centers and saddles in homoclinic networks are obtained, and the maximum numbers of sinks, sources, and saddles in homoclinic networks without centers are obtained as well. Such studies are to achieve global dynamics of planar polynomial dynamical systems, which can help one study global behaviors in nonlinear dynamical systems in physics, chemical reaction dynamics, engineering dynamics, and so on. This book is a reference for graduate students and researchers in the field of dynamical systems and control in mathematics, mechanical, and electrical engineering.
