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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