Skip to main content

Theory and Modern Applications

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