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0

Some thoughts: The 4-cycle finding code does not seem to actually reach a 4-cycle because FindRoot gives errors. The Take in your first bifurcation code takes the first 15 time steps. I think you want to take the last ones. Here's a chaotic-looking result, taking the last 50 steps: ListPlot[bifurcationPoints[1.53, 2.85, 270, 250]] Your system seems to ...

2

Following the traditional way parms = {EIL -> 4.31671*10^(-15), EIR -> 1.29501*10^(-14), \[Mu]L -> 3.2106*10^(-9), \[Mu]R -> 9.6318*10^(-9), bleg -> 1.5*10^(-6), b -> 4.5*10^(-6), m -> 7.5*10^(-6), L -> 22.5 10^(-6)}; eqnL = \[Phi]L''''[x] - \[Mu]L /EIL \[Omega]^2 \[Phi]L[x] == 0; eqnR = \[Phi]R''''[x] - \[Mu]R /EIR \[Omega]^2 \[Phi]...

6

I have a package that implements solving eigenvalue problems, including interface problems like this. First we need to install (first time only): Needs["PacletManager`"] PacletInstall["CompoundMatrixMethod", "Site" -> "http://raw.githubusercontent.com/paclets/Repository/master"] And then load it: Needs["...

1

Not sure how useful this is, but how about plotting what happens to a grid of values in one time step? map[{x_, y_}] := { x + .01 (0.4 x^3 - .2 y^2 x + 1.1 y^3), y + .01 (-9 x^3 + 9 x y^2 + .6 y^3)}; GraphicsRow[{ Show[ ListLinePlot[ Table[Table[{x, y}, {y, -3, 3, 0.25}], {x, -3, 3, 0.25}], PlotStyle -> Table[RGBColor[1 - x, 0, x], {x, ...

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For discrete data you can do it by "hand". Here is how to proceed. First we need some discrete data. You may make a Table, where you give explicit x/y values. E.g. Table[x^2, {x,{1,2,3}}] This would result in: {1,4,9} With this you may create data describing the velocity field of the form {point, velocity-vector}. E.g. dat = Flatten[ Table[{{x,...

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What do you mean by "plot the nonlinear difference equations"? I assume that you want, analogously to differential equations, to get a "velocity field". Towards this aim, you need to calculate the difference between x/y at n and n+1. Therefore you must not include the first x and y. In addition, your code has several syntax errors, I ...

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