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Two-dimensional Self and Product Cubic Systems, Vol. II: Crossing-linear and Self-quadratic Product Vector Field de Albert C. J. Luo

Two-dimensional Self and Product Cubic Systems, Vol. II: Crossing-linear and Self-quadratic Product Vector Field

Autor Albert C. J. Luo
en Limba Engleză Hardback – 10 sep 2024
This book is the thirteenth of 15 related monographs on Cubic Dynamical Systems, discusses self- and product-cubic systems with a crossing-linear and self-quadratic products vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed through up-down saddles, third-order concave-source (sink), and up-down-to-down-up saddles infinite-equilibriums. The author discusses how equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows exist in such cubic systems, and the corresponding switching bifurcations obtained through the inflection-source and sink infinite-equilibriums. In such cubic systems, the appearing bifurcations are:
saddle-source (sink)
hyperbolic-to-hyperbolic-secant flows
double-saddle
third-order saddle, sink and source
third-order saddle-source (sink)
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Specificații

ISBN-13: 9783031595738
ISBN-10: 3031595734
Pagini: 222
Ilustrații: Approx. 220 p.
Dimensiuni: 155 x 235 mm
Ediția:2024
Editura: Springer Nature Switzerland
Colecția Springer
Locul publicării:Cham, Switzerland

Cuprins

Self and Product Cubic Systems.- Double-saddles, Third-order Saddle nodes.- Vertical Saddle-node Series and Switching Dynamics.- Saddle-nodes and third-order Saddles Source and Sink.- Simple equilibrium networks and switching dynamics.

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 thirteenth of 15 related monographs on Cubic Dynamical Systems, discusses self- and product-cubic systems with a crossing-linear and self-quadratic products vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed through up-down saddles, third-order concave-source (sink), and up-down-to-down-up saddles infinite-equilibriums. The author discusses how equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows exist in such cubic systems, and the corresponding switching bifurcations obtained through the inflection-source and sink infinite-equilibriums. In such cubic systems, the appearing bifurcations are:
saddle-source (sink)
hyperbolic-to-hyperbolic-secant flows
double-saddle
third-order saddle, sink and source
third-order saddle-source (sink)
  • Develops a theory of self and product cubic systems with a crossing-linear and self-quadratic products vector field;
  • Presents equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows with switching by up-down saddles;
  • Shows equilibrium appearing bifurcations of various saddles, sinks, and flows.

Caracteristici

Develops a theory of self and product cubic systems with a crossing-linear and self-quadratic products vector field Presents equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows with switching by up-down saddles Shows equilibrium appearing bifurcations of various saddles, sinks, and flows