How to solve these types of circuits?

[subhadeepbiswas!]

I've followed the trace of a LED fader PCB which consist of an OPAMP (LM358) and some resistors, a trim pot , capacitor and a transistor and made a schematic out of it.
From the schematic what I can see is an integrator and a comparator. 47K resistance acting as a voltage divider to provide reference voltage to pin 3 and 6 of the OPAMP.
I simulated the circuit in multisim and found that it is generating a low frequency ramp signal from pin 1 (output of OPAMP1) which is connected to the base of the transistor.
I'm not able to get a clear concept on this. Mainly the feedback paths of the two OPAMPs as well as the functions of 100k, 30k resistors and 20k pot. Please guide me to understand the whole circuit in details. Thank you

[Zero999]

It's a relaxation oscillator. The comparator has hysteresis, so the high level threshold is greater than the low level threshold and the integrator is inverting and the forms the delay element of the circuit.
http://www.falstad.com/circuit/e-triangle.html

The comparator can be reconfigured, so it inverts the signal and the integrator replaced with a simple RC circuit, but it will produce a ramped waveform, rather than a triangle.
https://en.wikipedia.org/wiki/Relaxation_oscillator

There's nothing to limit the maximum current through the LEDs which isn't good. It would be better to use a constant current driver for the LEDs, rather than connecting them to an emitter follower.