Atkins cuts out the bodies fuel. If you are looking to diet and excercise, they are a bad combination.
As said above, Just eat small portions more often. And work out.
I eat first thing on a morning at 5.30, Go Running, Eat Cereals in work at 9am. Have a small meal at lunch, A healthy snack in the afternoon, A regular meal at night.
All healthy, All small. Keeps my body going. My excercise also consists of Elevated Pushups, Situps/Crunches, Pullups and Squats. I don't do weights. Although thats only because I don't have them. I'm not looking to be big, Just toned and unskinny
Bull, carbs should never have become the main fuel source for us. The western world has the most obesity and thats because firstly due to mass producing wheats, grains we all started to eat carbs as main food group decades ago which was bad. Then to lose weight everyone started eating low fat foods, which is even worse. The insulin spikes come from carb eating, insulin is problem.
The reason most people fail on a atkins or ketogenic diet is they eat a diet so different to normal, and so horrible to maintain that when they go off it they eat so radically differently and simply eat to much and most suddenly hit carbs again, which reintroduces the insulin cycle, carbs in, with low insulin resistance, massive blood sugar level drops, body craves sugar, eat more carbs, etc, etc. eating way over maintainance calories.
Ketogenic diets are great for fat loss, no carbs isn't really necessary, but low carbs is, however this can be different, some people have to eat under 20grams a day in general, some 30, some 50grams which makes it signifcantly easier. When the bulk of your main carlories comes from fat, the body uses fat for energy over carbs or eating muscle. Which means when you run out of freely available daily intake fat, its way easier to eat excess body fat as your body is basically in the right state to eat fat. WHen you eat mostly carbs and then run out, the body finds it easier to first eat muscle, than fat, so a high fat diet is actually the easiest way to lose fat. Atkins I'm not 100% sure on but I think he goes with the idea of eating however much you want, as long as its not carbs? A proper ketogenic weight loss diet is still a less calories in than calories burnt in a day, but still high fat and also the right types.
Calories in < calories burnt is important, but type of calories in is also very important. Low/no carb after 1-2 days also normally causes a lack of really feeling hungry as you don't get the high/low blood sugar which actually makes it a very easy diet to follow in terms of cravings, but difficult depending on what types of foods you normally eat/like to eat and what you have to eat on the diet. Frankly, you shouldn't eat that many carbs on a normal diet, on a training/bulking diet carbs are still bad, and you should eat most of your daily carbs before and after exercise not throughout the day.
look up timed carb and carb cycling diets for healthy ways to eat trying to lose weight, gain weight, whatever you want.