Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Regions $R$ of initial conditions

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,∞)
( $A_{1} = B_{1} = 0$ , $A_{2} \neq 0$ ) or ( $A_{2} = B_{2} = 0$ , $A_{1} \neq 0$ )	[0,∞)×(0,∞)
( $A_{1} = C_{1} = 0$ , $A_{2} \neq 0$ ) or ( $A_{2} = C_{2} = 0$ , $A_{1} \neq 0$ )	(0,∞)×[0,∞)
$A_{1} = B_{1} = 0$ , $A_{2} = B_{2} = 0$	[0,∞)×(0,∞)
$A_{1} = C_{1} = 0$ , $A_{2} = C_{2} = 0$	(0,∞)×[0,∞)
$A_{1} = C_{1} = 0$ , $A_{2} = B_{2} = 0$	[0,∞)×[0,∞)∖(0,0)
$A_{1} = B_{1} = 0$ , $A_{2} = C_{2} = 0$	[0,∞)×[0,∞)
( $A_{1} = 0$ , $B_{1} \neq 0$ , $C_{1} \neq 0$ ) or ( $A_{2} = 0$ , $B_{2} \neq 0$ , $C_{2} \neq 0$ )	[0,∞)×[0,∞)∖(0,0)

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