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Two-dimensional Crossing and Product Cubic Systems, Vol. I de Albert C. J. Luo

Two-dimensional Crossing and Product Cubic Systems, Vol. I

Autor Albert C. J. Luo
en Limba Engleză Hardback – 30 ian 2025
This book is the twelfth of 15 related monographs on Cubic Systems, discusses self and product cubic systems with a self-linear and crossing-quadratic product vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed. The volume explains how the equilibrium series with connected hyperbolic and hyperbolic-secant flows exist in such cubic systems, and that the corresponding switching bifurcations are obtained through the inflection-source and sink infinite-equilibriums. Finally, the author illustrates how, in such cubic systems, the appearing bifurcations include saddle-source (sink) for equilibriums and inflection-source and sink flows for the connected hyperbolic flows, and the third-order saddle, sink and source are the appearing and switching bifurcations for saddle-source (sink) with saddles, source and sink, and also for saddle, sink and source.
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Specificații

ISBN-13: 9783031595813
ISBN-10: 3031595815
Pagini: 252
Ilustrații: V, 220 p.
Dimensiuni: 160 x 241 x 19 mm
Greutate: 0.59 kg
Ediția:2024
Editura: Springer
Locul publicării:Cham, Switzerland

Cuprins

Self and product cubic systems.- Second and third order equibriliums.- Equilibrium series and switching dynamics.-  Saddle nodes and hyperbolic flow series.- Simple equilibrium series 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, the twelfth of 15 related monographs on Cubic Systems, discusses self and product cubic systems with a self-linear and crossing-quadratic product vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed. The volume explains how the equilibrium series with connected hyperbolic and hyperbolic-secant flows exist in such cubic systems, and that the corresponding switching bifurcations are obtained through the inflection-source and sink infinite-equilibriums. Finally, the author illustrates how, in such cubic systems, the appearing bifurcations include saddle-source (sink) for equilibriums and inflection-source and sink flows for the connected hyperbolic flows, and the third-order saddle, sink and source are the appearing and switching bifurcations for saddle-source (sink) with saddles, source and sink, and also for saddle, sink and source.
  • Develops a theory of self and product cubic systems with a self-linear and crossing-quadratic product vector field;
  • Presents equilibrium series with flow singularity and connected hyperbolic and hyperbolic-secant flows;
  • Shows equilibrium series switching bifurcations through a range of sources and saddles on the infinite-equilibriums.