پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 691 |
| تعداد مقالات | 10,035 |
| تعداد مشاهده مقاله | 71,039,328 |
| تعداد دریافت فایل اصل مقاله | 62,488,787 |
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 | ||
|
[1] D. Boularas, A new classification of planar homogeneous quadratic systems, Qual. Theory Dyn. Syst. 2(1) (2001) 93–110. [2] T. Date, Classification and analysis of two-dimensional real homogeneous quadratic differential equation systems, J. Diff. Equ. 32(3) (1979) 311–334. [3] J. Llibre, J. S. P. del Rio and J. A. Rodr´ıguez, Structural stability of planar homogeneous polynomial vector fields: applications to critical points and to infinity, J. Diff. Equ. 125(2) (1996) 490–520. [4] L.S. Lyagina, The integral curves of the equation y ′ = ax2 + bxy + cy2dx2 + exy + fy2 , Uspekhi Mat. Nauk 6(2) (1951) 171–183. [5] L. Markus, Quadratic differential equations and non-associative algebras, Ann. Math. Stud. 45(5) (1960) 185–213. [6] M. Nadjafikhah and M. Mirafzal, Classification the integral curves of a second degree homogeneous ODE, Math. Sci. 4(4) (2010) 371–381. [7] C.S. Sibirskii, Algebraic Invariants of Differential Equations and Matrices, Schtiintsa, Kishinev, Moldova (in Russian), 1976. [8] C.S. Sibirskii, Introduction to The Algebraic Theory of Invariants of Differential Equations, Nonlinear Science, Theory and Applications, Manchester University Press, 1988. [9] Z. Zhi-Fen, D. Tong-Ren, H. Wen-Zao and D. Zhen-Xi, Qualitative Theory of Differential Equations, American Mathematical Soc. 2006. | ||
|
آمار تعداد مشاهده مقاله: 15,812 تعداد دریافت فایل اصل مقاله: 9,347 |
||