04183nam a22005895i 4500 978-3-031-62810-8 DE-He213 20251030114941.0 cr nn 008mamaa 250212s2024 sz | s |||| 0|eng d 9783031628108 978-3-031-62810-8 10.1007/978-3-031-62810-8 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 Crossing-Variable Cubic Nonlinear Systems [electronic resource] / by Albert C. J. Luo. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. X, 386 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 crossing-cubic vector fields -- Crossing-linear and crossing-cubic vector fields -- Crossing-quadratic and crossing-cubic Vector Field -- Two crossing-cubic vector fields. This book is the fourth of 15 related monographs presents systematically a theory of crossing-cubic nonlinear systems. In this treatment, at least one vector field is crossing-cubic, and the other vector field can be constant, crossing-linear, crossing-quadratic, and crossing-cubic. For constant vector fields, the dynamical systems possess 1-dimensional flows, such as parabola and inflection flows plus third-order parabola flows. For crossing-linear and crossing-cubic systems, the dynamical systems possess saddle and center equilibriums, parabola-saddles, third-order centers and saddles (i.e, (3rd UP+:UP+)-saddle and (3rdUP-:UP-)-saddle) and third-order centers (i.e., (3rd DP+:DP-)-center, (3rd DP-, DP+)-center) . For crossing-quadratic and crossing-cubic systems, in addition to the first and third-order saddles and centers plus parabola-saddles, there are (3:2)parabola-saddle and double-inflection saddles, and for the two crossing-cubic systems, (3:3)-saddles and centers exist. Finally, the homoclinic orbits with centers can be formed, and the corresponding homoclinic networks of centers and saddles exist. Readers will learn new concepts, theory, phenomena, and analytic techniques, including · Constant and crossing-cubic systems · Crossing-linear and crossing-cubic systems · Crossing-quadratic and crossing-cubic systems · Crossing-cubic and crossing-cubic systems · Appearing and switching bifurcations · Third-order centers and saddles · Parabola-saddles and inflection-saddles · Homoclinic-orbit network with centers · Appearing bifurcations 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 Multibody systems. 66046 Vibration. 66047 Mechanics, Applied. Dynamics. 65524 Nonlinear theories. 65525 Engineering mathematics. 64145 Engineering Data processing. Waves, instabilities and nonlinear plasma dynamics. 69750 Multibody Systems and Mechanical Vibrations. 66048 Applied Dynamical Systems. 65530 Mathematical and Computational Engineering Applications. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031628092 Printed edition: 9783031628115 Printed edition: 9783031628122 https://doi.org/10.1007/978-3-031-62810-8 ZDB-2-PHA ZDB-2-SXP 66686 66686