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Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II: A Crossingvariable Cubic Vector Field de Albert C. J. Luo

Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II: A Crossingvariable Cubic Vector Field

Autor Albert C. J. Luo
en Limba Engleză Hardback – 12 sep 2024
This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows.  The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. 
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: 9783031571077
ISBN-10: 303157107X
Pagini: 200
Ilustrații: V, 197 p. 44 illus., 40 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.57 kg
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, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows.  The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. 
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
  • Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations;
  • Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations;
  • Explains infinite-equilibriums for the switching of the first-order sink and source flows. 

Caracteristici

Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations Explains infinite-equilibriums for the switching of the first-order sink and source flows