Two-dimensional Product-Cubic Systems, Vol. IV

This book, the eighth of 15 related monographs, discusses a product-cubic dynamical system possessing a product-cubic vector field and a crossing-univariate quadratic vector field. It presents equilibrium singularity and bifurcation dynamics, and . the saddle-source (sink) examined is the appearing bifurcations for saddle and source (sink). The double-inflection saddle equilibriums are the appearing bifurcations of the saddle and center, and also the appearing bifurcations of the network of saddles and centers. The infinite-equilibriums for the switching bifurcations featured in this volume include:

• Parabola-source (sink) infinite-equilibriums,
• Inflection-source (sink) infinite-equilibriums,
• Hyperbolic (circular) sink-to source infinite-equilibriums,

• Hyperbolic (circular) lower-to-upper saddle infinite-equilibriums.

  Develops a theory of cubic dynamical systems having a product-cubic vector field and a crossing-quadratic vector field Shows equilibriums and paralleled hyperbolic and hyperbolic-secant flows with switching though infinite-equilibriums Presents CCW and CW centers separated by a paralleled hyperbolic flow and positive and negative saddles

  Autorentext

  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.

  Inhalt

Preface .- Crossing-quadratic and product-cubic systems.- Double-inflection-saddles and bifurcation dynamics.- Parabola-saddles and bifurcation.