Classification of singular points of perturbed quadratic systems

	Classification of singular points of perturbed quadratic systems
International Journal of Nonlinear Analysis and Applications
دوره 12، شماره 2، بهمن 2021، صفحه 1817-1825 اصل مقاله (784.53 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2018.13063.1672
نویسندگان
Asadollah Aghajani^* ؛ Mohsen Mirafzal
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844-13114, Iran
چکیده
We consider the following two-dimensional differential system: \[ \left\{\begin{array}{l} \dot{x}=ax^{2}+bxy+cy^{2}+\Phi(x,y) \,, \\ \dot{y}=dx^{2}+exy+fy^{2}+\Psi(x,y) \,, \end{array} \right.\] 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.
کلیدواژه‌ها
Quadratic system؛ Classification of singular points؛ Poincare index
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