You probably have
lawn grubs. If you roll back the turf, you should be able to get a good count of how many there are in the brown patches. Lawn grubs induce many people to break out the chemicals, but permies have a better way: nematodes. Nematodes are part of the soil biology and when there are not enough of them, other critters can thrive. Conversely, if there is a high population of nematodes (like you add a whole bunch), other critters that spend a lot of time in the soil are going to have a difficult go of it.
You can cultivate your own nematodes, which is explained in
this post, but if you don't want to spend the time and effort to do that, you can go down to
Home Depot and get a small bucketful from them. When applying nematodes, you have to remember that they are alive. They are not some chemical that can be stored on the shelf and mixed with all sorts of solvents and blown out through pressure sprayers. Carefully read and follow the instructions for application and soon you will have millions of friends taking care of your lawn grub problem for you.