Two-dimensional Product Cubic Systems, Vol. VII: Self- Quadratic Vector Fields (Two-dimensional Product Cubic Systems, 7) - Hardcover

Über die Autorin bzw. den Autor

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.

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This book, the seventh of 15 related monographs, concerns nonlinear dynamics and singularity of cubic dynamical systems possessing a product-cubic vector field and a self-univariate quadratic vector field. The equilibrium singularity and bifurcation dynamics are discussed. The saddle-source (sink) is the appearing bifurcations for saddle and source (sink). The double-saddle equilibriums are the appearing bifurcations of the saddle-source and saddle-sink, and also the appearing bifurcations of the network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations include:

• inflection-saddle infinite-equilibriums,

• hyperbolic-source (sink) infinite-equilibriums,

• up-down (down-up) saddle infinite-equilibriums,

• inflection-source (sink) infinite-equilibriums.

• Develops a theory of cubic dynamical systems possessing a product-cubic vector field and a self-quadratic vector field;
• Finds series/networks of equilibriums, 1-dimenional hyperbolic/hyperbolic-secant flows, finite-equilibrium switching;
• Presents sink and source separated by a connected hyperbolic-secant flow, and the (SO,SI) and (SI,SO)-saddles.