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Theory and Modern Applications

Table 4 Signs of slopes of E 1 and E 2 in B when C 1 >0 or B 2 >0

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

 

B i γ i C i β i , i = 1,2

B i α i A i β i , i = 1,2

C i α i A i γ i , i = 1,2

Slope of E 1

Slope of E 2

(i)

=0

>0

>0

+

(ii)

=0

<0

<0

+

(iii)

>0

≥0

≥0

+ or −

(iv)

>0

≥0

<0

+

(v)

>0

<0

<0

+

+ or −

(vi)

<0

≥0

≥0

+ or −

(vii)

<0

<0

≥0

+

(viii)

<0

<0

<0

+ or −

+