{"product_id":"two-dimensional-self-and-product-cubic-systems-vol-i-von-albert-c-j-luo","title":"Two-dimensional Self and Product Cubic Systems, Vol. I","description":"\n                                \n                \u003cp\u003eThis 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:\u003c\/p\u003e\n                                \n                \n                \u003cul\u003e\n                                        \t\n                    \n                    \u003cli\u003e double-inflection saddles, \u003c\/li\u003e\n                                        \t\n                    \n                    \u003cli\u003e inflection-source (sink) flows,\u003c\/li\u003e\n                                        \t\n                    \n                    \u003cli\u003e parabola-saddles (saddle-center),\u003c\/li\u003e\n                                        \t\n                    \n                    \u003cli\u003e third-order parabola-saddles, \u003c\/li\u003e\n                                        \t\n                    \n                    \u003cli\u003e third-order saddles (centers),\u003c\/li\u003e\n                                        \t\n                    \n                    \u003cli\u003e third-order saddle-source (sink).\u003c\/li\u003e\n                                        \n                \n                \u003c\/ul\u003e\n                                \n                \n                \u003cp\u003e \u003c\/p\u003e\n                                \n                \n                \u003cp\u003e \u003c\/p\u003e\n                                \n                \n                \u003cp\u003e \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031570957\"\u003e\u003ch3\u003eSelf-linear and Crossing-quadratic Product Vector Field\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Hardcover - 9783031570957","offer_id":53701780111685,"sku":"9783031570957","price":171.19,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/91a0531f-98ed-4f9f-8df9-1a9ccf30e1ed.jpg?v=1775966836","url":"https:\/\/shop.autorenwelt.de\/products\/two-dimensional-self-and-product-cubic-systems-vol-i-von-albert-c-j-luo","provider":"Autorenwelt Shop","version":"1.0","type":"link"}