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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 | ||
| تاریخ دریافت: 21 آبان 1396، تاریخ پذیرش: 07 اردیبهشت 1397 | ||
| 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 | ||
| مراجع | ||
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