{"product_id":"two-dimensional-crossing-variable-cubic-nonlinear-systems-von-albert-c-j-luo","title":"Two-dimensional Crossing-Variable Cubic Nonlinear Systems","description":"\n                                \n                \u003cp\u003eThis book is the fourth of 15 related monographs presents systematically a theory of crossing-cubic nonlinear systems. In this treatment, at least one vector field is crossing-cubic, and the other vector field can be constant, crossing-linear, crossing-quadratic, and crossing-cubic. For constant vector fields, the dynamical systems possess 1-dimensional flows, such as parabola and inflection flows plus third-order parabola flows. For crossing-linear and crossing-cubic systems, the dynamical systems possess saddle and center equilibriums, parabola-saddles, third-order centers and saddles (i.e, (3rd UP+:UP+)-saddle and (3rdUP-:UP-)-saddle) and third-order centers (i.e., (3rd DP+:DP-)-center, (3rd DP-, DP+)-center) . For crossing-quadratic and crossing-cubic systems, in addition to the first and third-order saddles and centers plus parabola-saddles, there are (3:2)parabola-saddle and double-inflection saddles, and for the two crossing-cubic systems, (3:3)-saddles and centers exist. Finally,the homoclinic orbits with centers can be formed, and the corresponding homoclinic networks of centers and saddles exist.\u003c\/p\u003e\n                                \n                \n                \u003cp\u003eReaders will learn new concepts, theory, phenomena, and analytic techniques, including\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Constant and crossing-cubic systems\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Crossing-linear and crossing-cubic systems\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Crossing-quadratic and crossing-cubic systems\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Crossing-cubic and crossing-cubic systems\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Appearing and switching bifurcations\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Third-order centers and saddles\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Parabola-saddles and inflection-saddles\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Homoclinic-orbit network with centers\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e· Appearing bifurcations\u003c\/p\u003e\n                                \n                \n                \u003cp\u003e \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031628092\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Hardcover - 9783031628092","offer_id":54154583212357,"sku":"9783031628092","price":160.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/5316b174-c833-4af1-943a-86714d6a40d6.jpg?v=1772774900","url":"https:\/\/shop.autorenwelt.de\/products\/two-dimensional-crossing-variable-cubic-nonlinear-systems-von-albert-c-j-luo","provider":"Autorenwelt Shop","version":"1.0","type":"link"}