{"product_id":"two-dimensional-self-independent-variable-cubic-nonlinear-systems-von-albert-c-j-luo","title":"Two-dimensional Self-independent Variable Cubic Nonlinear Systems","description":"\n                                \n                \u003cp\u003eThis book, the third of 15 related monographs, presents systematically a theory of self-independent cubic nonlinear systems. Here, at least one vector field is self-cubic, and the other vector field can be constant, self-linear, self-quadratic, or self-cubic. For constant vector fields in this book, the dynamical systems possess 1-dimensional flows, such as source, sink and saddle flows, plus third-order source and sink flows.  For self-linear and self-cubic systems discussed,  the dynamical systems possess source, sink and saddle equilibriums, saddle-source and saddle-sink, third-order sink and source (i.e, (3rd SI:SI)-sink and (3rdSO:SO)-source) and third-order source (i.e., (3rd SO:SI)-saddle, (3rd SI, SO)-saddle) . For self-quadratic and self-cubic systems, in addition to the first and third-order sink, source and saddles plus saddle-source and saddle-sink, there are (3:2)-saddle-sink and (3:2) saddle-source and double-saddles. For the two self-cubic systems, (3:3)-source, sink and saddles exist. Finally, the author describes that homoclinic orbits without centers can be formed, and the corresponding homoclinic networks of source, sink and saddles exists.   \u003c\/p\u003e\n                                \n                \n                \u003cp\u003e\n                                        Readers will learn new concepts, theory, phenomena, and analytic techniques, including\n                    \n                    \u003cbr\u003e\n                                        Constant and crossing-cubic systems\n                    \n                    \u003cbr\u003e\n                                        Crossing-linear and crossing-cubic systems\n                    \n                    \u003cbr\u003e\n                                        Crossing-quadratic and crossing-cubic systems\n                    \n                    \u003cbr\u003e\n                                        Crossing-cubic and crossing-cubic systems\n                    \n                    \u003cbr\u003e\n                                        Appearing and switching bifurcations\n                    \n                    \u003cbr\u003e\n                                        Third-order centers and saddles\n                    \n                    \u003cbr\u003e\n                                        Parabola-saddles and inflection-saddles\n                    \n                    \u003cbr\u003e\n                                        Homoclinic-orbit network with centers\n                    \n                    \u003cbr\u003e\n                                        Appearing bifurcations\n                \n                \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031571145\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783031571114\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783031571145","offer_id":56520660058437,"sku":"9783031571145","price":160.49,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783031571114","offer_id":53669638635845,"sku":"9783031571114","price":160.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/c6240cac-36b7-4692-9ac0-c42b59f06380.jpg?v=1775968595","url":"https:\/\/shop.autorenwelt.de\/en\/products\/two-dimensional-self-independent-variable-cubic-nonlinear-systems-von-albert-c-j-luo","provider":"Autorenwelt Shop","version":"1.0","type":"link"}