The term “triune brain” describes three levels of the brain; the reactive brain (brainstem), the feeling brain (limbic), and the thinking brain (neo-cortex). When anxiety arises the reactive brain takes over, and we become more instinctive in our action.
This understanding of the brain plays a role in Bowen’s Family Systems Theory, which focuses on being “less-anxious” presence (the correct phrase is “non-anxious presence,” but we are only non-anxious when we are dead), attempting to allow the thinking brain to function even when the anxiety in the surroundings is running high.
National Institute of Neurological Disorders and Stroke offers a good overview of the brain on their website, called Brain Basics: Know Your Brain.