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Global analyses of a class of cubic systems

Authors:

Li Jinming Cai Suilin

Institution:

(1) Department of Applied Mathematics, Zhejiang University, 310027 Hangzhou, China

Abstract:

In this paper, we use the canonical forms of homogeneous polynomials of degree 3 to study the global properties of cubic systems

$\dot x = x + P_3 (x,y),\dot y = y + Q_3 (x,y)$

WhereP ₃ andQ ₃ are homogeneous polynomials of degree 3 inx, y. Through this work, we draw an overall outline of such systems. Supported by the National Natural Science Foundation of China, No. 19371069

Keywords:

Phase-portrait Limit cycle Cubic systems

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