03037nam a22005415i 4500 978-981-97-2204-4 DE-He213 20251030114617.0 cr nn 008mamaa 241214s2024 si | s |||| 0|eng d 9789819722044 978-981-97-2204-4 10.1007/978-981-97-2204-4 doi QA843-871 GPFC bicssc MAT034000 bisacsh GPFC thema Luo, Albert C. J. author. aut http://id.loc.gov/vocabulary/relators/aut 81241 1-dimensional Flow Arrays and Bifurcations in Planar Polynomial Systems [electronic resource] / by Albert C. J. Luo. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. IX, 377 p. 49 illus., 48 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Constant and Self variable Polynomial Systems -- Constant and Crossing variable Polynomial Systems -- Single univariate Polynomial Systems -- Higher order Infinite equilibrium Bifurcations. This book introduces to 1-dimensional flow arrays and bifurcations in planar polynomial systems. The 1-dimensional source, sink and saddle flows are discussed, as well as the 1-dimensional parabola and inflection flows. The singular source, sink and saddle flows are the appearing and switching bifurcations for simple sink and source flow arrays and for lower-order singular source, sink and saddle flow arrays. The singular parabola and inflection flows are the appearing and switching bifurcations for simple parabola arrays and also for lower-order singular parabola and inflection flow arrays. The infinite-equilibriums in single-variable polynomial systems are also discussed, which are the appearing and switching bifurcations of hybrid arrays of source, sink, and saddle flows with parabola and inflections. This book helps readers understand the global dynamics of planar polynomial systems and the Hilbert sixteen problem. Dynamical systems. Differential equations. System theory. 66519 Control theory. 68675 Dynamical Systems. Differential Equations. Complex Systems. 66520 Systems Theory, Control. 68676 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819722037 Printed edition: 9789819722051 Printed edition: 9789819722068 https://doi.org/10.1007/978-981-97-2204-4 ZDB-2-SMA ZDB-2-SXMS 65706 65706