COMPUTING GENERAL FORM OF THE FOCAL VALUE AND LYAPUNOV FUNCTION FOR THE LOPSIDED SYSTEM IN DEGREE EIGHT

Hero W. Salih , Abdeljalil Nachaoui (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

In this paper, Concerned with planer autonomous system lopsided system of degree eight. We find the general form of all the focal values $\eta_k$ (k is even and $k \geq 2$) and the Lyapunov function $V (x; y)$ for the lopsided system degree eight. As the type to find the maximum number of limit cycles which can be bifurcate out of the origin and the necessary and sufficient conditions for the existence of a center we need to compute the focal values $\eta_{2k+2}, the Lyapunov quantities $L(k)$ and Lyapunov function $V (x; y)$.

Mots clés: Lopsided system; Focal value; Lyapunov quantities; Lyapunov function

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Hero W. Salih, Abdeljalil Nachaoui. COMPUTING GENERAL FORM OF THE FOCAL VALUE AND LYAPUNOV FUNCTION FOR THE LOPSIDED SYSTEM IN DEGREE EIGHT. Advanced Mathematical Models & Applications, 2020, 5 (1), pp.121-130. ⟨hal-02587797⟩