A quintic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:msub> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> -equivariant Liéna

We continue the study a quintic Z 2 -equivariant Liénard system x ˙ = y , y ˙ = − ( a 0 x + a 1 x 3 + a 2 x 5 ) − ( b 0 + b 1 x 2 ) y with a 2 b 1 ≠ 0 , arising from the complex Ginzburg-Landau equation. The global dynamics of this system have been investigated in Chen et al. (2023) [6] when the sum of the indices of all equilibria is −1, i.e., a 2 < 0 . The aim of this paper is to study the global dynamics of this quintic Liénard system when the sum of the indices of all equilibria is 1, i.e., a 2 > 0 . Notice that the dynamics in the case a 2 > 0 are richer and more complex compared to the case when a 2 < 0 .