You are showing a picture with a frequency response, but this sort of problem cannot be analyzed like this, anymore. An
.AC analysis linearizes the circuit, but a saturating inductor is anything but. So, the only way to see it is to simulate it in time-domain. Or on the breadboard, be sure to bring protective gear...
Here's an attempt in LTspice using the nonlinear Chan core, with some bogus values (for exemplification, only). The first picture shows what an
.AC analysis would look like:
Which shows a nice, smooth response, two docile poles. If you switch over to a
.TRAN analysis, and make it a frequency sweep (from
fmax) with a high enough amplitude (see
Which, again, looks innocent enough, but when you check out the current through the inductor, here's what you get:
Below is the whole simulation, and the above three show details in three sections around the beginning, middle, and end. You can clearly see that the beginning (3rd row) and the end (1st row) are low in distortions, but the middle is not only distorted, but also high valued. As @winny and @jonk say, in simplistic terms, the inductance drops, hence the current rises, but relative to the waveform shape. And the transition is related to the hysteresis of the core. You can think of it in terms of a
tanh() curve: the slope around zero is smooth and quasi-linear, but when you get to saturation, the value along the x-axis (magnetic field strength) rises very abruptly with the slightest y-axis (magnetic flux density).