Theory and Modern Applications
From: The roles of conic sections and elliptic curves in the global dynamics of a class of planar systems of rational difference equations
Parameter condition
R
A 1 >0, A 2 >0
[0,∞)×[0,∞)
( A 1 = B 1 =0, A 2 ≠0) or ( A 2 = B 2 =0, A 1 ≠0)
[0,∞)×(0,∞)
( A 1 = C 1 =0, A 2 ≠0) or ( A 2 = C 2 =0, A 1 ≠0)
(0,∞)×[0,∞)
A 1 = B 1 =0, A 2 = B 2 =0
A 1 = C 1 =0, A 2 = C 2 =0
A 1 = C 1 =0, A 2 = B 2 =0
[0,∞)×[0,∞)∖(0,0)
A 1 = B 1 =0, A 2 = C 2 =0
( A 1 =0, B 1 ≠0, C 1 ≠0) or ( A 2 =0, B 2 ≠0, C 2 ≠0)