{"product_id":"twodimensional-crossing-product-polyno","title":"Twodimensional Crossing \u0026 Product Polyno By Luo, Albert C. J.","description":"This book is about hybrid networks of singular and non-singular, one-dimensional flows and equilibriums in crossing and product polynomial systems. The singular equilibriums and one-dimensional flows with infinite-equilibriums in product polynomial systems are presented in the theorem. The singular equilibriums are singular saddles and centers, parabola-saddles, and double-inflection-saddles. The singular one-dimensional flows are singular hyperbolic-flows, hyperbolic-to-hyperbolic-secant flows, inflection-source and sink flows, and inflection-saddle flows. The higher-order singular one-dimensional flows and singular equilibriums are for the appearing bifurcations of lower-order singular and non-singular one-dimensional flows and equilibriums. The infinite-equilibriums are the switching bifurcations for two associated networks of singular and non-singular, one-dimensional flows and equilibriums. The corresponding mathematical conditions are presented, and the theory for nonlinear dynamics of crossing 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 flows and equilibriums are completed, and the sampled networks of non-singular one-dimensional flows and equilibriums are presented in this book.    ","brand":"MediaPlace","offers":[{"title":"Default Title","offer_id":58260431700350,"sku":"NW9789819657148","price":108.97,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1379\/1261\/files\/9789819657148.jpg?v=1792401243","url":"https:\/\/mediaplace.com\/products\/twodimensional-crossing-product-polyno","provider":"MediaPlace","version":"1.0","type":"link"}