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Two-dimensional Crossing-Variable Cubic Nonlinear Systems, Vol IV de Albert C. J. Luo

Two-dimensional Crossing-Variable Cubic Nonlinear Systems, Vol IV

Autor Albert C. J. Luo
en Limba Engleză Hardback – 17 sep 2024
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
 
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Specificații

ISBN-13: 9783031628092
ISBN-10: 3031628098
Ilustrații: X, 360 p. 31 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:2024
Editura: Springer Nature Switzerland
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

Dr. Albert C. J. Luo is a Distinguished Research Professor at the Southern Illinois University Edwardsville, in Edwardsville, IL, USA. Dr. Luo worked on Nonlinear Mechanics, Nonlinear Dynamics, and Applied Mathematics. He proposed and systematically developed: (i) the discontinuous dynamical system theory, (ii) analytical solutions for periodic motions in nonlinear dynamical systems, (iii) the theory of dynamical system synchronization, (iv) the accurate theory of nonlinear deformable-body
dynamics, (v) new theories for stability and bifurcations of nonlinear dynamical systems. He discovered new phenomena in nonlinear dynamical systems. His methods and theories can help understanding and solving the Hilbert sixteenth problems and other nonlinear physics problems. The main results were scattered in 45 monographs in Springer, Wiley, Elsevier, and World Scientific, over 200 prestigious journal papers, and over 150 peer-reviewed conference papers.

Textul de pe ultima copertă

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.

Caracteristici

​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