03656nam a22005655i 4500 978-3-031-57112-1 DE-He213 20251030113302.0 cr nn 008mamaa 241108s2024 sz | s |||| 0|eng d 9783031571121 978-3-031-57112-1 10.1007/978-3-031-57112-1 doi QC718.5.W3 PHFP bicssc SCI055000 bisacsh PHFP thema Luo, Albert C. J. author. aut http://id.loc.gov/vocabulary/relators/aut 81241 Two-dimensional Self-independent Variable Cubic Nonlinear Systems [electronic resource] / by Albert C. J. Luo. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. X, 275 p. 33 illus., 32 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Constant and Self-Cubic Vector fields -- Self-linear and Self-cubic vector fields -- Self-quadratic and self-cubic vector fields -- Two self-cubic vector fields. This book is the third of 15 related monographs, presents systematically a theory of self-cubic nonlinear systems. Here, at least one vector field is self-cubic, the other vector fields can be constant, self-linear, self-quadratic, and self-cubic. For constant vector fields in this book, the dynamical systems possess 1-dimensional flows, such as source, sink and saddle flows, plus third-order source and sink flows. For self-linear and self-cubic systems, the dynamical systems possess source, sink, and saddle equilibriums, saddle-source and saddle-sink equilibriums, third-order source and sink (i.e., ( 3rdSO:SO)-source, ( 3rdSI:SI)-sink) and third-order saddle (i.e., (3rdSO:SI)-saddle, 3rdSI:SO)-saddle). For self-quadratic and self-cubic systems, in addition to the first and third-order source, sink, saddles plus saddle-source, saddle-sink, there are (3,2)-saddle-sink, (3,2)-saddle-source and double-saddles, and for the two self-cubic systems, double third-order source, sink and saddles exist. Finally, the authors describes thar the homoclinic orbits without cen-ters can be formed, and the corresponding homoclinic networks of source, sink and saddles exist. • Develops equilibrium singularity and bifurcations in 2-dimensional self-cubic systems; • Presents (1,3) and (3,3)-sink, source, and saddles; (1,2) and (3,2)-saddle-sink and saddle-source; (2,2)-double-saddles; • Develops homoclinic networks of source, sink and saddles. . Plasma waves. 69749 Dynamics. 65524 Nonlinear theories. 65525 Mechanics, Applied. Multibody systems. 66046 Vibration. 66047 Waves, instabilities and nonlinear plasma dynamics. 69750 Applied Dynamical Systems. 65530 Engineering Mechanics. Multibody Systems and Mechanical Vibrations. 66048 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031571114 Printed edition: 9783031571138 Printed edition: 9783031571145 https://doi.org/10.1007/978-3-031-57112-1 ZDB-2-PHA ZDB-2-SXP 64779 64779