Skip to main content

Advertisement

Table 2 Some formulas for T 1 ( x n , y n ) and T 2 ( x n , y n ) for which system ( 1 ) is bounded

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

  Number of terms in the denominator of T i ( x n , y n ), i = 1,2 Formula for the denominator of T i ( x n , y n ), i = 1,2 Formula for T i ( x n , y n ), i = 1,2, for which system (1) is bounded
1. Three A i + B i x n + C i y n α i A i + B i x n + C i y n , β i x n A i + B i x n + C i y n , γ i y n A i + B i x n + C i y n , α i + β i x n A i + B i x n + C i y n , α i + γ i y n A i + B i x n + C i y n , β i x n + γ i y n A i + B i x n + C i y n , α i + β i x n + γ i y n A i + B i x n + C i y n
2. Two B i x n + C i y n β i x n + γ i y n B i x n + C i y n , β i x n B i x n + C i y n , γ i y n B i x n + C i y n
A i + B i x n α i A i + B i x n , β i x n A i + B i x n , α i + β i x n A i + B i x n
A i + C i y n α i A i + C i y n , γ i y n A i + C i y n , α i + γ i y n A i + C i y n
3. One A i α i / A i
B i x n β i / B i
C i y n γ i / C i