@Carl Love Sorry; I realized that afterward. As you say, the is() returning false in the original question remains puzzling, though I guess in some sense it is false for n = 2.5. Since the product in term2 doesn't evaluate to any simpler expression, it's hard to see why it doesn't always return FAIL.

@AHSAN As I said, "So I expect u(y) to go to 1 at y=1 and to have a slope of zero at y=0, both of which seem to be true from your plots." Perhaps I don't understand what you mean by start at zero - for me that means that u = 0 at y=0. But depending on the curve, u is in the range 0.45..0.5 at y=0, which is not zero and not 1.

@AHSAN For u(y), which is D(psi)(y) you have

D(psi)(1 + x^2/2) = 1, D(D(psi))(0) = 0

So I expect u(y) to go to 1 at y=1 and to have a slope of zero at y=0, both of which seem to be true from your plots.

@AHSAN You say theta(y) and phi(y) should start from 1, but you have

D(theta)(1 + x^2/2) = 1, theta(0) = 0,
D(phi)(1 + x^2/2) = 1, phi(0) = 0

so I expect theta and phi to start from zero and have a slope of 1 at y = 1 (since x=0).

I don't use Safari, so can't comment about browser issues. But if I go into my account information, I can change my email address and keep the same account. So I suggest you ask technical support to change your account to another email address. Then logging on with that email address and using the forgotten password mechanism should solve that problem.

@Math-dashti

 true.mw

@mehdi jafari OK, see @mmcdara's answer for why this is hard to do. (I was confused by your terminology since I do not consider finding where FF(x,P1) = 0 to be "plotting the function FF".)

@Math-dashti Like this?

Download solve.mw

@mmcdara The worksheet opens with the comma's but executing it changes them to ".", but the plot error is the same owing to complex values. 

@Math-dashti I don't understand exactly what you want - please specify in the notation of your worksheet exactly what you want. I think S__1 and S__2 are some functions of p1,p2,p3,k? If so I don't know what  functions those are and what you want to do with them?

Or if you want to reproduce the paper results, please give a worksheet with that notation.

@Andiguys As I said, the view option is the syntax to magnify it. but it isn't helpful in this case.

@Math-dashti S__1 and S__2 are not mentioned in the picture you supplied so I do not know what you are asking.

Yes, you cannot plot complex values on a real plot. Don't you want to reject complex equilibria? Aren't only real u(t), v(t) of interest?

@mmcdara  I tried to reproduce the behaviour in a minimal example for an scr, but things are different in 2025 from 2024, so I am giving up on this.

@Math-dashti For a chaotic system we may expect the solution to be very sensitive to the type of solver and step size algorithm so it is not surprising that Matlab and Maple give somewhat different results.

Edit: I see you used different parameters for the two cases. But I can't reproduce Fig 1a even approximately, so I think there is a typo somewhere in the paper.

@mmcdara Your chaotic-2_mmcdara_4.mw works in 2024:

chaotic-2_mmcdara_4_2024.mw

In the earlier behaviour, there was a complicated interaction where range+refine worked the solution up to a point, then suggested increasing maxfun to go beyond that point, but then gave a warning and didn't work if maxfun was too high. But without parameters it worked with those same settings (see other reply). Range and refine work with other ODEs, e.g. the Van der Pol one in the odeplot help page, so it is something about accuracy, which you solved with relerr.