The hypothalamus, along with the pituitary, is in charge of the neuroendocrine system that releases neurotransmitters. These neurotransmitters increase (excite) or decrease ( inhibit) electrical activity in neurons. Increases or decreases in neurotransmitters have a major impact on mood and behavior.
The hypothalamus produces the the hormones that effect the pituitary gland. Once the amygdala senses danger the sympathetic branch of the autonomic system is alerted and the hypothalamus, through the pituitary, releases hormones that travel to the adrenal glands. This is where cortisol is released (please see posts on the autonomic nervous system and cortisol.) Cortisol increases the level of glucose in the blood to respond to the threat.
Under normal circumstances the threat passes and the cortisol levels return to normal. However many people who have ongoing anxiety live with ongoing increased cortisol levels. This is one of the places Somatic Experiencing is so helpful; it helps people to regulate their autonomic nervous system, decreasing the spiked activity in the sympathetic branch. I have helped many performers-and many others as well-to self regulate; it makes a huge difference in their daily and artistic lives.