Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212220210701Classification of singular points of perturbed quadratic systems18171825531910.22075/ijnaa.2018.13063.1672ENAsadollahAghajaniSchool of Mathematics, Iran University of Science and
Technology, Narmak, Tehran 16844-13114, IranMohsenMirafzalSchool 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<br /> $Delta=(af-cd)^{2}-(ae-bd)(bf-ce)neq0 $.<br /> By calculating Poincare index and using Bendixson formula we will find all the possibilities under definite conditions<br /> 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