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Table 3 Global dynamics for α 1 =0 and α 2 =0 when E 1 and E 2 are pairs of parallel lines

From: The roles of conic sections and elliptic curves in the global dynamics of a class of planar systems of rational difference equations

Parameter region E 0 E 1 E 2 E 3
β 1 A 1 <0
γ 2 A 2 <0
G.A.S.
Basin of attraction:
[ 0 , ) 2
β 1 A 1 >0
γ 2 A 2 0
Saddle
Its stable manifold:
Positive y-axis
L.A.S.
Basin of attraction:
( 0 , ) 2 and positive x-axis
β 1 A 1 0
γ 2 A 2 >0
Saddle
Its stable manifold:
Positive x-axis
L.A.S.
Basin of attraction:
( 0 , ) 2 and positive y-axis
β 1 A 1 >0
γ 2 A 2 >0
Repeller Saddle
Its stable manifold:
Positive x-axis
Saddle
Its stable manifold:
Positive y-axis
L.A.S.
Basin of attraction:
( 0 , ) 2