Beyond the "living dead" theory, zombies are characterized primarily by their abnormal but sterotyped behaviours. We can see this particularly in many popular Hollywood movies, where zombies aren't portrayed as reanimated dead, but as living humans infected by a biological pathogen such as a virus. They are alive, but different. However the method of transmission, the person is usually transformed into a single-minded hunting machine with all changes to bodily function serving to locate the prey, capture them and then to feed.
Neuroscience has shown that all thoughts and behaviors are associated with neural activity within the brain. Therefore, the zombie brain would also be similar. It makes no sense for it to be different. Because of the behavioural symptoms shown in movies, we're given clues and can piece some of the them together.
Let's break it down by symptoms:
1. Rage: When you look at zombies, they are always trying to eat people (generally angry I guess if they are to feel something). It's an anger that is directed toward everyone simply because they're human or, the next meal course. According to Oscillatory Thoughts, this behaviour has roots in the primitive parts of the brain that center around flight or fight. In humans not infected, these impulses are suppressed by signals in the lower part of the frontal lobe: the orbitofrontal cortex. It sends inhibitory signals to the amygdala.
Like crocodiles (who is driven by the amygdala--studies show that by damaging it, the flight or fight responses is significantly reduced) zombies would be driven by this. Working with the amygdala, the anterior cingulate cortex dampens the excitability, giving the frontal lobe time to process and think what to do. A zombie would potentially have a damaged anterior cingulate cortex. With it affected, the zombie would be unable to regulate the anger, creating hyper-aggression.
2. Appetite: In the brain, there is an important part that controls feeding. This is the ventromedial hypothalamus. Zombies have an insatiable appetite it seems. They're always hunting for prey to chew on. If zombies were to have damage in this area, they wouldn't know when to stop eating. There have been studies in primates that have shown that damage to this area of the brain causes monkeys to eat anything and uncontrollably.
3. Stumbling/staggering gait:
A zombie isn't the best athlete. They stumble and stagger as they move. The area in the brain responsible for balance and fluid motion is the cerebellum and the basal ganglia. Zombies would probably suffer from some sort of dysfunction, much like cerebellar degeneration such as ataxia.
It's possible that all combined, this could explain the behaviour of zombies. Or at least the ones we know from popular fiction. What other symptoms can you think of?