Periodic solutions for first-order cubic non-autonomous differential equation with bifurcation analysis. Issue 1 (1st January 2020) - Akram, Saima; Nawaz, Allah; Yasmin, Nusrat; Kalsoom, Humaira; Chu, Yu-Ming
Abstract : 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 z = 0 . Periodic solutions with polynomial coefficients are executed for classes C 10, 3, C 10, 4, and C 10, 5 . Limit cycles are found for both non-homogeneous and homogeneous polynomials with trigonometric coefficients for classes C 22, 11, C 24, 12 and C 10, 10, respectively. We developed a formula ϰ 10, which is not available in literature. By using our newly developed formula, we succeeded to find highest known multiplicity 10 for the classes C 10, 3, C 10, 4 with algebraic and C 10, 10, C 24, 12 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.