TY  - BOOK
AU  - Luo,Albert C.J.
ED  - SpringerLink (Online service)
TI  - 1-dimensional Flow Arrays and Bifurcations in Planar Polynomial Systems
SN  - 9789819722044
AV  - QA843-871 
PY  - 2024///
CY  - Singapore
PB  - Springer Nature Singapore, Imprint: Springer
KW  - Dynamical systems
KW  - Differential equations
KW  - System theory
KW  - Control theory
KW  - Dynamical Systems
KW  - Differential Equations
KW  - Complex Systems
KW  - Systems Theory, Control
N1  - Constant and Self variable Polynomial Systems -- Constant and Crossing variable Polynomial Systems -- Single univariate Polynomial Systems -- Higher order Infinite equilibrium Bifurcations
N2  - 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
UR  - https://doi.org/10.1007/978-981-97-2204-4
ER  -