EDL (often referred to as Electronic Traction Control.)
This system is used by the VW GTI-VR6 (FWD) and Mercedes ML320 (AWD) and probably others.
It's the poor man's LSD. (Some people dislike my characterization of it, as it can be very finely tuned, but it's still very cheap to implement and has some reliability problems.)
This is an electronically regulated speed sensitive system using the two independent ABS channels. Start with an open differential and go back to Example 3. You're holding onto the right output shaft while the input shaft turns. Now add a disc brake and rotor on the left input shaft.
Engage EDL. When the computer senses a speed imbalance between left and right, (remember the left shaft is spinning at 2X and the right is not moving at all), it simply applies the brakes to the left side output shaft. The open differential immediately tries to balance the torque. You will feel it trying to turn the right side immediately. If it can grab the left harder than you're holding the right (which it most certainly can and will) then it'll immediately transfer some rotation to the right output shaft and it will twist out of your hand. If you could hold onto the right side hard enough (weld it the side of a tractor trailer truck) , it would be forced to slip the left brake disc, or stall the engine.

In practice, the engine will not stall because the maximum resistance is simply whatever it takes to move the mass of the car, or spin the other tire. So if one side is spinning and the other side has traction, then the EDL will slow the spinning side, and the torque transfers to the side with greater traction and either that side spins or the car moves.

Now, all my examples have been pretty extreme. The EDL doesn't actually stop anything. It simply slows it down until the speed difference is equalized, and it does this by pulsing the ABS channels maybe a dozen times a second. It switches off when the speed differential is low enough.

Also note, it does not try to prevent wheelspin! If both sides lose traction at the same time and spin at the same speed then EDL has no idea anything is wrong. A more advanced system measures the difference between the speeds of all 4 wheels during acceleration and assumes that anything spinning faster than the slowest rotating wheel is slipping. A cheap system will apply the brakes. An expensive system will reduce the throttle until the problem goes away. BMW's and new VW's use this method to prevent wheelspin.

The problem with the way EDL works is that it's pretty harsh. The pulsing of the ABS isn't progressive. If the ABS is on, it applies full braking power followed by zero braking power.. full, zero, full, zero.. The torque from the engine that's being transferred repeatedly all the way across the drivetrain from wheel to wheel a dozen times a second, puts stress on everything. Brakes, rotors, axles, U joints, output shafts, and the differential itself. The left and right halves of the differential in the VW 02A transmission are held together with rivets which if forced to take this pounding too long will eventually fail. Neat huh?
Did I mention EDL uses the brakes? Perhaps "uses up the brakes" would be more appropriate. It's really designed for emergency low traction situations and not drag racing or rallying or other long duration, low traction situations.

So why use EDL if it's so bad?
Well, the torque transfer is only really bad if the input torque is high and the resistance at the side where it's being transferred to is high. Such as.. When you're spinning one tire on the pavement and the engine is cranking out 175 ft/lbs of torque. When it kicks that torque across from one side to the other, it finds that the other side (also on pavement) initially has lots of traction and therefore a lot of resistance which means that the drivetrain takes the brunt of the stress all at once. Worse case, is when the side that is slowed, slows enough to regain full traction, while the other side starts spinning. Then the EDL compensates and brakes that side.. and the whole process repeats back and forth many times.. Solution.. take your foot off the gas.

On the other hand, if one tire is on snow, and the other is spinning on ice and the EDL has you accelerating slowly, the engine is producing little torque and if you tried to gas it hard, the torque transfer from the EDL meets up with little resistance on the snow so the torque "escapes" as wheelspin on the snow side. If it's ice and pavement then yes, you want to avoid mashing on the gas, but pulling away smoothly shouldn't present a problem as each pulse of the ABS transfers into a small bit more acceleration of the car.

Should I worry when the EDL kicks in?. The ABS and diff can't transfer any more torque through the drivetrain than the engine supplies and the best case traction resistance allows. If traction is low on both sides, and power is high the traction is the limiting factor to how much drivetrain stress is induced. Otherwise, if one side had good traction on only one side, then just don't hammer the gas. If you're spinning the tires on dry pavement, expect TFS. Simple.

Quattro, Quaife, Torsen, Peloquin: (Torque Biasing Differentials)
Audi's Quattro and the popular aftermarket Quaife systems use a set of worm gears inside the differential in place of the spider gears, which bind up when there's a resistive torque imbalance. That means, as long as both sides show equal resistance then they are free to rotate at different speeds, such as when going around a turn.

The whole thing is called a "Torsen" system as in "Torque Sensing" (Torsen is actually a Quaife trademark, and the more generic term is Torque Biasing Differential or TBD) because it instantly reacts to torque imbalance transferring power to the wheels that can use it most. There's a difference between the two main torsen diffs. Quattro used something developed by Gleason called invex gearing which is is really all about worm gears. A torque imbalance causes it to *try* to turn the low traction output shaft faster than the higher traction side, but that would cause the invex spider gears to turn, and they drive worm gears which have a greater mechanical advantage (due to the angle of the teeth) than the output sun gears have on the worm gears. That means that a multiple of the torque that would have gone to the low traction side actually goes to the high traction side. So if 20 ft-lbs of traction is at the low traction side, something like 80 ft-lbs goes to the side that can actually use it. A ratio of 4 to 1 or 5 to 1 is common but changing the gear teeth angles changes the ratio. The Quaife uses helical gears to accomplish exactly the same thing, but the actual operation is not nearly as easy to understand. Somehow the helical gears float in pockets on the inside of the housing and apply radial and axial forces generated by the angle of the gear teeth. It can be tuned just like the invex gears to vary the torque ratio. Note however that without significant preload either torsen diff will not work well with a wheel completely off the ground. 0 ft-lbs time 4 is still 0. A simple braking trick helps though. (Note, the EDL system discussed above, actually works pretty well with a torsen diff. It activates rarely, but allows for much greater torque transfer when it does.) For this reason, they're rarely found on 4WD vehicles, the notable exception being the original Hummer, which has a note in the owner's manual explaining how to use the brakes and gas at the same time, should one or more tires be off the ground.

It is capable of going from an open differential to say 60% locked differential condition absolutely instantly (zero lag), so many would argue that it's about as close to perfect as it gets for performance driving. There are no clutches to wear out. Several AWD systems like the Quattro system put a torsen diff in the center of the car to control slip between front and rear wheels. This system does not have the problem the VC does with the ABS. A torsen diff only distributes torque when it's under load. When it's freewheeling all the wheels can turn at different speeds as the ABS may desire.
(Note: It looks like the current Audi Quattro system only uses the torsen diff in the center, and some other LSD or EDL at the axles. )

The disadvantages are that the mechanism is a bit heavier, more mechanically complicated thus expensive, and can't be tuned or adjusted dynamically. Plus, it reacts so fast and is so even handed that it literally makes a torsen diff equipped AWD car boring when you'd really like to hang it all out. If you want to go 100mph in the snow nothing beats Quattro. If you want to slide sideways or spin and recover, forget it. I've heard that VW's new 4motion system is much more fun because of its electronic control.

BTW, I do think that a Torsen Differential in a front wheel drive car is a good thing. If you plan on putting a blower on your engine, get a Quaife. If you want to drag race, get a Quaife. If you worry about EDL hammering and TFS a lot, get a Quaife. It'll help you put down power on a twisty road, and reduces torque steer. I finally bought a Quaife clone from the machinist Gary Peloquin that makes my FWD GTI VR6 a joy to drive fast around sharp corners while full on the throttle, which is not normally fun in a higher powered FWD car.

So there it is.