Luo, Albert C. J. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access X, 275 p. 33 illus., 32 illus. in color. online resource. 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. . 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. by Albert C. J. Luo. Plasma waves Dynamics Nonlinear theories Mechanics, Applied Multibody systems Vibration Waves, instabilities and nonlinear plasma dynamics Applied Dynamical Systems Engineering Mechanics Multibody Systems and Mechanical Vibrations QC718.5.W3 9783031571121 https://doi.org/10.1007/978-3-031-57112-1 https://doi.org/10.1007/978-3-031-57112-1 241108 20251030113302.0 978-3-031-57112-1