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A criterion for the monotonicity of the ratio of two Abelian integrals in piecewise-smooth differential systems | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 15، شماره 6، شهریور 2024، صفحه 1-17 اصل مقاله (630.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28713.3976 | ||
| نویسندگان | ||
| Rasoul Asheghi* 1؛ Rasool Kazemi2؛ Ghadeer Mohammad3 | ||
| 1Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111. | ||
| 2Department of Mathematical Sciences, Kashan University, Kashan, Iran | ||
| 3Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111. | ||
| تاریخ دریافت: 24 مهر 1401، تاریخ پذیرش: 19 تیر 1402 | ||
| چکیده | ||
| In this paper, we present a new criterion function for investigating the monotonicity of the ratio of two Abelian integrals in piecewise-smooth differential systems, and then, apply it to deal with some examples. More precisely, we consider the Abelian integrals of the form \begin{equation*} I_{k}(h)=\oint_{\Gamma_{h}}f_{k}(x)ydx,\hspace{0.5cm} k=0,1, \end{equation*} with $\Gamma_{h}=\Gamma_{h}^{L}+\Gamma^{R}_{h}$, where $\Gamma^{L}_{h}=\{(x,y)\in \mathbb{R}^{2}| \frac{1}{2}y^2+\Psi_{2}(x)=h, \ x<0 \}$ and $\Gamma_{h}^{R}=\{(x,y)\in \mathbb{R}^{2}| \frac{1}{2}y^2+\Psi_1(x)=h,\ x>0 \}$. We prove that the monotonicity of the presented criterion function implies the monotonicity of the ratio $\frac{I_1(h)}{I_0(h)}$ and provide a few examples to explain the application of this criterion. | ||
| کلیدواژه‌ها | ||
| Piecewise-smooth differential systems؛ Melnikov function؛ Monotonicity؛ Abelian integral؛ Limit cycle | ||
| مراجع | ||
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