Journal of Taibah University for Science ( IF 2.8 ) Pub Date : 2020-08-26 , DOI: 10.1080/16583655.2020.1810429 Saima Akram 1 , Allah Nawaz 1 , Nusrat Yasmin 1 , Humaira Kalsoom 2 , Yu-Ming Chu 3
This article deals with the development of the number of periodic solutions for ordinary differential equations. We investigated focal values for first-order non-autonomous differential equation for periodic solutions from a fine focus . Periodic solutions with polynomial coefficients are executed for classes and Limit cycles are found for both non-homogeneous and homogeneous polynomials with trigonometric coefficients for classes , and , respectively. We developed a formula , which is not available in literature. By using our newly developed formula, we succeeded to find highest known multiplicity 10 for the classes with algebraic and with trigonometric coefficients. We present a variety of polynomial classes along with their bifurcation analysis which confirms the generality and authenticity of the method presented.
中文翻译:
一阶三次非自治微分方程具有分岔的周期解
本文讨论了常微分方程周期解数的发展。我们从精细焦点出发研究了周期解的一阶非自治微分方程的焦点值。对类执行具有多项式系数的周期解 和 发现非三角多项式和齐次多项式的极限环 , 和 , 分别。我们制定了一个公式,这在文献中没有。通过使用我们新开发的公式,我们成功地找到了类别的已知最高多重性10 与代数和 与三角系数。我们提出了各种多项式类别及其分叉分析,这证实了所提出方法的一般性和真实性。