New Cat Behavior Issues

So, about a week ago, I went for a walk around the neighborhood and I saw a young cat sitting in the street. I went over, and after a minute, it came up and let me pet it. Well, it ended up just following all the way all the way home. And I have asked around and posted about finding a cat, no owner has been found yet. Anyway.. He's a real sweet cat, playful and everything. Except, after a while of petting him, and I mean having him just sit on my lap and me not holding on to him, JUST petting him, he starts growling and showing aggression. Why is this? And it there any way to correct it? Unles I REALLY have to, I don't want to end up bringing him to a shelter and being put down or something. So, if anyone can help, I'd appreciate it.

He is just overstimulated.  You can learn to recognize signs that he is... Such as a spasm going up or down his back or his ears might fold back or he might tense up and dig his claws in a little bit.  These all mean "OK, I've reached my loving limit for the time being.  Put me down and let me be for a few minutes."  Just put him down.  It happens with a lot of cats.  You'll learn soon enough to recognize his signals. 

Like P3 says. Cats have a limit, just like people. I am guessing he didn't actually attack you, right? It was a warning. In all likeliness you have just missed the first few signs/warnings the cat gave you and it resulted in him making it as clear as possible. It doesn't mean he is false or aggressive. It's really not behavior you would have to correct.

My boy Anyon reaches his limits too. Sometimes he's fine staying in my lap, but after a while he wants me to stop petting him. You can see it in the ears, or when his tail starts flicking every time you stroke. If I stop petting, he will stay in my lap, if I don't he leaves.

You must also not forget that you are new to him. A week is a very short time. Cats do not usually get comfortable with new humans and/or homes so fast. That he snuggles up with you at all is a very big thing. Don't expect him to trust you so fast. Big chance that the intensity of his warnings grow less over time. Like I said, my boy just gets annoyed and leaves. He knows I wouldn't hurt him or force him to stay, so the warning isn't needed (anymore).

Plus, just another small thing. As you know nothing of his past, there are a number of things that could also contribute to it. Who knows where he's been or what he's seen. Just be patient. As long as he does not actually attack, you can assume he just doesn't know and trust you enough. And you need to learn to read him.

He sounds very sweet, by the way. Enjoy en good luck!

@Jinjer321996, I just want to say that from the five cats I've petted, this is completely normal. Cats only want to be pet up to a certain point before it becomes "overstimulation" as P3andTheKing said. I've gotten a bite to tell me to stop repeatedly before from maybe four out of the five cats. I think the big one just moved away, but the others would quickly bite without breaking the skin to tell me to stop.

I hope you keep this cat! Just search for more information on normal cat behavior and post questions. That's what I'm doing. I do love my kitty!