That's what I wanted to know, is it the simulator or there's really oscillation.
Max scale zooms in to the signal.
I have to learn to use ltspice, this isn't working...
Yeah I have to build it on breadboard and test it out. the problem is I don't have a decent oscilloscope to analyze it in depth. just a cheap chinese one, that's why I was trying to use a simulator...
Yes, I noticed the link could easily be missed, so I went back and enlarged it. In that case, it's just noise i.e. rounding errors in the simulation. You'll often see similar things in real life, when zooming in on a signal very closely, especially with a digital oscilloscope. What oscilloscope do you have? Some of the cheap Chinese ones are perfectly decent.
The circuit you originally attached appears to oscillate and experience tells me it's likely to do so, because it has two amplifiers in each loop, especially as one of them is open-loop. Sometimes this is a necessary evil, or it's is just easier to design that way, but in this case it isn't: you've already got a current source going to the base of the Darlington pair and ORing diodes, so you might as well connect the output of each amplifier to each of them.
Why is LTSpice not working? I know it depends on what one is familiar with, but I find it infinity easier to use than that falstad simulator, which made me curse and swear after a few minutes of editing your schematic. If it was in LTSpice, I would have been able to mirror it, with the input to output going left to right, but there doesn't seem to be a way to do that with falstad, without redrawing it.