<p>This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:</p><p>-&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;double-inflection saddles,&#xa0;</p><p>-&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;inflection-source (sink) flows,</p><p>-&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;parabola-saddles (saddle-center),</p><p>-&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;third-order parabola-saddles,&#xa0;</p><p>-&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;third-order saddles and centers.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

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

  • Albert C. J. Luo

摘要

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:

-        double-inflection saddles, 

-        inflection-source (sink) flows,

-        parabola-saddles (saddle-center),

-        third-order parabola-saddles, 

-        third-order saddles and centers.