Great question Lara. No, plants do not have brains or a nervous system BUT they may have something similar.
The brain and the nervous system are defined by science as consisting of special cells called neurons which pass messages to the brain and the neurons in the brain then process these messages. Plants do not have neurons in their structure. So if a plant can feel, communicate and maybe solve problems it is achieved by something other than the brain.
Lots of scientists have/are looking at plants and their behaviours. There is good evidence that plants can communicate with each other, trees (and maybe other plants) even have their own internet. Not a conventional network but an internet of fungi. It has been discovered that the fungi ‘roots’ called mycelium (they are not really roots …they are the main part of the fungi, the thing we see is just the ‘fruit’) create a network of filaments in the soil stretching great distances and connect to other plants around them. Researchers have found that trees communicate information on food, insects and other dangers to each other using this network..
There is a lot we do not know about plants.
A question. Suppose you had access to ten trees and a mycelium network. What experiment would you setup to test the ideas about the trees communicating and helping each other.
Hope this helped. Need further help then please ask another question or make a comment.
(Anyone reading this post who wants to ask a question or make a comment please feel free to do so)
Revised 9/9/17 Added ‘A question.’ Last para.