Houseplants and pest management

I used to call Sorrel "shamrock" because that's what it looks like: the leaves are parted into 3 leaflets, each one sort of heart-shaped. There's a low-growing, creeping plant that grows commonly in my area in addition to sorrel:


Purslane. Is this it?
Purslane! I've always had it growing in the cracks of cement and was surprised to find it was good to eat!
 
It was a long time before I learned it is edible. I like it, and let it grow on my property now (if I'm not hungry). Between my former rabbits and myself, my property has been depleted of such delicacies as dandelions and lamb's-quarters. :drool:

They also liked common plantain (at least they preferred it to grass or hay) but I didn't.
 
I do not poison animals labelled as 'pests' from 'taking over' my plants.
If they are attracted to the plant, you would then be stuck in a cycle of killing more and more as time went on!
That is not sensible at all in my view.
Can I stop any plants from totally being taken over?
To a certain extent with care, for example around where I plant rosemary and lavender there are fewer ants due to the smell they are repelled from.
 
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