Limit cycles for a class of polynomial differential systems

Qiao Jianyuan; Shui Shuliang

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Limit cycles for a class of polynomial differential systems

机译：一类多项式微分系统的极限环

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摘要

In this paper, we consider the limit cycles of a class of polynomial differential systems of the form $dot{x}=-y^{2p-1}, dot{y}=x^{2mp-1}+arepsilon(px^{2mp}+qy^{2p})(g(x,y)-A)$, where $g(x,y)$ is a polynomial. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of a center using the averaging theory of first order.

机译：在本文中，我们考虑了以下形式的多项式极限系统的极限环：$ dot {x} =-y ^ {2p-1}， dot {y} = x ^ {2mp-1} + varepsilon（px ^ {2mp} + qy ^ {2p}）（g（x，y）-A）$，其中$ g（x，y）$是多项式。我们使用一阶平均理论从中心的周期性轨道中得出分叉的最大极限环数。

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《Electronic Journal of Qualitative Theory of Differential Equations》 |2016年第4期|共9页
作者
Qiao Jianyuan; Shui Shuliang;
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中图分类数学;
关键词
limit cyclespolynomial differential systemsaveraging theory$(pq)$-trigonometric functions;

机译：极限环多项式微分系统平均理论$（pq）$-三角函数;

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3. On the Limit Cycles of a Class of Generalized Kukles Polynomial Differential Systems via Averaging Theory [J] . Amar Makhlouf, Amor Menaceur International Journal of Differential Equations . 2015,第Null期

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4. Centers and limit cycles in polynomial systems of ordinary differential equations [C] . Valery G. Romanovski, Douglas S. Shafer School on Real and Complex Singularities . 2016

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5. On the maximum number of limit cycles of certain polynomial Lienard equations. [D] . Yao, Leummim. 1995

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7. On the limit cycles for a class of discontinuous piecewise cubic polynomial differential systems [O] . Bo Huang 2020

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8. Co-Existence of Centers and Limit Cycles in Polynomial Systems [R] . Kooij, R. E., Zegeling, A. 1996

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Limit cycles for a class of polynomial differential systems

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