Bifurcation diagram for coupled nonlinear difference equations

I’ve been trying to plot bifurcation diagram of 2D map following the example by Chris K in here, where I managed to plot few of periodic cycles

EDIT

(*2-cycle*)
A = 1.6; b = 2.47; c = 0.9; d = 1.19;
EM[{x_, y_}] := {x + y + A x y - b x, y + x/A - x y + c y^2 - d y}
EM2[{x_, y_}] = Simplify[EM[EM[{x, y}]]];
j2 := D[EM2[{x, y}], {{x, y}, 1}]
eqq2 = FindRoot[EM2[{x, y}] == {x, y}, {{x, 1.3}, {y, 0.644}}]
Eigenvalues[j2 /. eqq2] (*{-2.6888, 0.0128774} eigenvalues *)
ListLinePlot[Transpose[NestList[EM, {x + 10^-4, y} /. eqq2, 100]]]

(* 4-cycle *)
EM4[{x_, y_}] = Simplify[EM[EM[EM[EM[{x, y}]]]]];
j4 := D[EM4[{x, y}], {{x, y}, 1}]
eqq4 = FindRoot[EM4[{x, y}] == {x, y}, {{x, 1.3}, {y, 0.644}}]
Eigenvalues[j4 /. eqq4] (*{11.6416, 0.00122683} eigenvalues *)
ListLinePlot[Transpose[NestList[EM, {x + 10^-4, y} /. eqq4, 100]]]

Here is the 2-cycle

and 4-cycle

From these results, I try to code few attempts to analyse its bifurcation diagram with $b,c,d$ is fixed.

EDIT from Chris’s advice, I made some adjustment on Take : which now take last 50 elements from the list.

bifurcationPoints[AStart_, AStop_, m_, n_] := 
Flatten[Table [{A, #} & /@ Take[Quiet@NestList[{#1[[1]] 
+ #1[[2]] + A #1[[1]] #1[[2]] - 2.47 #1[[1]], 
#1[[2]] + #1[[1]]/A - #1[[1]] #1[[2]] + 0.9 #1[[2]]^2 - 1.2 #1[[2]]} &, 
{1.3, 0.6}, n][[All, 1]], -50], 
{A, AStart, AStop, (AStop - AStart)/m}], 1]
ListPlot[bifurcationPoints[1, 2.85, 270, 300]]

the code is working, but need to make some adjustment on the parameters.

However, my expectation is the plot ($x_t, y_t$ againts $A$) would be something like this or here.

Thus, from those 1D examples (with some modification), I tried

EM[A_, b_, c_, d_][{x_,y_}] := {x + y + A x y - b x, y + x/A - x y + c y^2 - d y}
pts = 2000;  
ListPlot[Flatten[Table[Transpose[{Table[A, pts],NestList[EM[A, 2.47, 0.9, 1.2], 
Nest[EM[A, 2.47, 0.9, 1.2], {1.3, 0.6}, 2000], pts - 1]}], {A,1.4, 2.0, 0.01}], 1], 
PlotStyle -> {Black, Opacity[0.2], PointSize[0.001]}, 
AxesLabel -> {A, xy}]

and from this example, I tried

eq1 = x[t] == x[t - 1] + y[t - 1] + A x[t - 1] y[t - 1] - 2.47 x[t - 1];
eq2 = y[t] == y[t - 1] + x[t - 1]/A - x[t - 1] y[t - 1] + 0.9 y[t - 1]^2 - 1.2 y[t - 1];
ic = {x[0] == 1.3, y[0] == 0.6};
eqtry = Flatten[Table[sol = RecurrenceTable[{eq1, eq2, ic}, {X[t], Y[t]}, {t, 0, 10}];
Replace[DeleteDuplicates[Take[sol, -2]], {{X_ -> {a, X}}, {Y_ -> {a, Y}}},1], {a, 1.4, 2.0, 0.1}], 1]      
ListPlot[eqtry]

The range of A could be from $(0, 1.5]$, but the code unable to produced any result. I believe this due to the selected parameters

Any suggestion anyone? Thanks in advance!

ListPlot[bifurcationPoints[1.53, 2.85, 270, 250]]

A = 1.4;
ListLinePlot[Transpose[NestList[EM, {x + 10^-4, y} /. eqq2, 43]], 
 PlotRange -> All]