دانلود کتاب سیستم‌های چندجمله‌ای خود و حاصلضرب دوبعدی

This book is a monograph about hybrid networks of singular and nonsingular, one-dimensional _lows and equilibriums in self and product polynomial systems. The higher-order singular one-dimensional _lows and singular equilibriums are for the appearing bifurcations of lowerorder singular and non-singular one-dimensional _lows and equilibriums. The singular equilibriums are singular sinks, sources, and saddles, saddle-sinks, saddle-sources, and double-saddles. The singular one-dimensional _lows are singular hyperbolic _lows, hyperbolic-tohyperbolic- secant _lows, inflection-source and sink _lows, inflectionsaddle _lows. The infinite-equilibriums are the switching bifurcations for two associated networks of singular and non-singular, onedimensional _lows and equilibriums. The infinite-equilibriums include: increasing-to-decreasing inflection-sources (sinks), hyperbolicsources (sinks), hyperbolic-upper (lower) saddles, increasing-todecreasing inflection-upper (lower)-saddles; increasing (deceasing) inflection-sources (sinks), hyperbolic-tohyperbolic- secant sources (sinks), hyperbolic-to-hyperbolic-secant upper (lower)-saddles, increasing (decreasing) inflection-upper (lower)-saddles; increasing-to-deceasing concave-sources (sinks), asymptote-sinks (sources), asymptote-upper (lower)-saddles, increasing-todecreasing concave-upper (lower)-saddles; increasing (decreasing)-concave-sources (sinks), down (up)- asymptote sources (sinks), down (up)-asymptote upper (lower)- saddles, increasing (decreasing)-concave-upper (lower)-saddles. The corresponding mathematical conditions are presented, and the theory for nonlinear dynamics of self and product polynomial systems is presented through a theorem. The mathematical proof is completed through the local analysis and the first integral manifolds. The illustrations of singular one-dimensional _lows and equilibriums are completed, and the sampled networks of non-singular one-dimensional _lows and equilibriums are presented in this book. In this book, three chapters are included. Chapter 1 presents the nonlinear dynamics of singular _lows and equilibriums with the corresponding infinite-equilibriums in self and product polynomial systems through a theorem. The appearing and switching bifurcations based on the singular _lows and equilibriums, and infinite-equilibriums are presented. Chapter 2 proves the mathematical condition in the theorem through local analysis and the first integral manifolds. In Chap. 3, the singular one-dimensional _lows and singular equilibriums with infinite-equilibriums are presented for a better understanding of singular dynamics in self and product polynomial systems. In addition, hybrid networks of non-singular one-dimensional _lows and equilibriums are presented, and such hybrid networks appear, and two associated networks are switched through the singular one dimensional _lows and equilibriums with the infinite-equilibriums. Finally, the author hopes the materials presented herein can provide a better understanding of the extended Hilbert sixteen problems and the corresponding dynamics.