{"product_id":"two-dimensional-crossing-and-product-polynomial-systems-von-albert-c-j-luo","title":"Two-dimensional Crossing and Product Polynomial Systems","description":"\n                                \n                \u003cp\u003eThis 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.   \u003c\/p\u003e\n                                \n                \n                \u003cp\u003e \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789819657148\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Hardcover - 9789819657148","offer_id":58092634931525,"sku":"9789819657148","price":181.89,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/51cc8584-c972-4cf8-8489-f033327eb0ec.jpg?v=1779947021","url":"https:\/\/shop.autorenwelt.de\/en\/products\/two-dimensional-crossing-and-product-polynomial-systems-von-albert-c-j-luo","provider":"Autorenwelt Shop","version":"1.0","type":"link"}