The term “analog modelling” is pretty broad, anything can be termed a model of something no matter how bad the model is. A straight line can be said to model a circle under certain conditions, but when what you actually wanted was a circle and were given a straight line you wouldn’t be happy! So we don’t blame you if you think analog modelling plugins are a load of BS, since some of the stuff you’ve tried probably was.
Cytomic models circuits by preserving the location and connection of all the critical components in it. We use the same methods used in circuit simulators, but optimised to run fast. The continuous circuit equations are discretised using MNA (Modified Nodal Analysis) and then solved for using quasi Newton-Raphson iterations to converge on a solution. Equivalent circuits of groups of linear components are pre-computed to save CPU, along with a bunch of other optimisations so that the model can run hundreds of thousands of times per second. A normal circuit simulator can take 5 minutes or more to process one second of audio, our plugins do it in a fraction of a second otherwise your CPU would be maxed out!