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<p>Preface.- Crossing-linear and Self-quadratic Product Systems.- Double-saddles and switching dynamics.- Vertically Paralleled Saddle-source and Saddle-sink.- Horizontally Paralleled Saddle-source and Saddle-sink.- Simple Equilibrium Networks and Switching Dynamics.</p>

<p>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.<br></p><p><br></p><p></p><p>&nbsp;</p><br><p>&nbsp;</p><p>&nbsp;<br></p>

​This book, the tenth of 15 related monographs, discusses product-cubic nonlinear systems with two crossing-linear and self-quadratic products vector fields and the dynamic behaviors and singularity are presented through the first integral manifolds. The equilibrium and flow singularity and bifurcations discussed in this volume are for the appearing and switching bifurcations. The double-saddle equilibriums described are the appearing bifurcations for saddle source and saddle-sink, and for a network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations are also presented, specifically:<p>· Inflection-saddle infinite-equilibriums,</p><p>· Hyperbolic (hyperbolic-secant)-sink and source infinite-equilibriums</p><p>· Up-down and down-up saddle infinite-equilibriums,</p><p>· Inflection-source (sink) infinite-equilibriums.</p><p><ul><li>Develops a theory of nonlinear dynamics and singularity of crossing-linear and self-quadratic product dynamical systems;</li><li>Shows hybrid networks of singular/simple equilibriums and hyperbolic flows in two same structure product-cubic systems;</li><li>Presents network switching bifurcations through infinite-equilibriums of inflection-saddles hyperbolic-sink and source.</li></ul></p><p><br></p><p><br></p>

Develops a theory of nonlinear dynamics and singularity of crossing-linear and self-quadratic Shows hybrid networks of singular/simple equilibriums and hyperbolic flows in two same Presents network switching bifurcations through infinite-equilibriums of inflection-saddles hyperbolic-sink and source