Sugar cravings will probably be there for the first 3-5 days, but once you get past them it's all downhill from there. I believe that Dr. Atkins says to limit your consumption of artificial sweeteners of any kind to 2 or 3 packets a day on induction. Something that helps when cravings hit is to eat something high fat or high protein (or both). You can also try supplements such as chromium and L-Glutamine to help diminish cravings.
Just so you know, 1/2 cup of Splenda is 12 grams of carb (24 grams per cup), so don't forget to count them when you do use it for making sweet treats like cheesecake or muffins.
Dr. Atkins recommends avoiding aspartame mostly because of health concerns. Saccharin and sucralose are both permitted but still limited.
Many people find that eating things that taste sweet provoke sugar cravings and I think it makes it harder to get past the sugar cravings when you are feeding them with sweet tasting things. Even though it's not sugar, just the sweet taste can get your body craving more.
As always, these things are a YMMV (your mileage may vary) thing. Some people can use artificial sweeteners without any problems at all, but there's no way to tell how they affect you individually without trying them for yourself.