Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212220211101Classification of singular points of perturbed quadratic systems18171825531910.22075/ijnaa.2018.13063.1672ENAsadollah AghajaniSchool of Mathematics, Iran University of Science and
Technology, Narmak, Tehran 16844-13114, Iran0000-0003-0358-4518Mohsen MirafzalSchool of Mathematics, Iran University of Science and
Technology, Narmak, Tehran 16844-13114, IranJournal Article20171112We consider the following two-dimensional differential system:<br />\[ \left\{\begin{array}{l}<br />\dot{x}=ax^{2}+bxy+cy^{2}+\Phi(x,y) \,, \\<br />\dot{y}=dx^{2}+exy+fy^{2}+\Psi(x,y) \,,<br />\end{array} \right.\]<br />in which $\lim_{(x,y)\rightarrow(0,0)}\frac{\Phi(x,y)}{x^{2}+y^{2}} = \lim_{(x,y)\rightarrow(0,0)}\frac{\Psi(x,y)}{x^{2}+y^{2}}=0$ and $\Delta=(af-cd)^{2}-(ae-bd)(bf-ce)\neq0 $. By calculating Poincare index and using Bendixson formula we will find all the possibilities under definite conditions for classifying the system by means of kinds of sectors around the origin which is an equilibrium point of degree two.https://ijnaa.semnan.ac.ir/article_5319_0bfcf12a7266bea2f8c2cef980500468.pdf