Sympathetic & parasympathetic nervous system

Two major nervous system divisions are sympathetic/parasympathetic nervous system:
Sympathetic - flight, fight, freeze, submit (primarily associated with the Solar Plexus nerve) these are outside of voluntary control and slow down or inhibit digestion and elimination during stressful or traumatic experiences. The sympathetic nervous system is a sun energy which is fiery, stress and activation based. This solar energy within the body mobilizes the entire body, inhibits metabolic functions and reroutes energy. 
Parasympathetic - rest, digest, reproduce, heal, is associated with the 10th cranial nerve known as the Vagus nerve. This nerve originates at the base of the brain and exits the skull just behind and below the ears. It connects to the organs of speech, swallowing in the throat then passes to the heart and lungs where it separates into R & L and continues to the diaphragm coming together front and back in the abdomen (liver, small and large intestines & stomach). The parasympathetic nervous system is moon energy which is calming & nurturing based. This cooling energy within the body soothes the body, redistributes energy and promotes metabolic function.
These two major nervous system divisions come together in the Mani Pura Chakra located at the navel center and influence our mind and consciousness directly. This is the energy center that is responsible for functions of: 
personal power
pranic source and strength,
protection
We embody these qualities in the organs, connective tissue and nerves in the abdomen.
One pranayama that balances the sympathetic and parasympathetic nervous system is alternate nostril breathing.

Alternate Nostril Breathing - Anuloma Viloma
In this Breathing Practice, you inhale through one nostril, possibly hold the breath, and then exhale through the other nostril. The left nostril is the channel of energy called Ida and the right nostril is the channel of energy called Pingala. Anuloma Viloma (alternate nostril breath) restores, equalizes and balances the flow of Prana (Life Force energies) in the body. Alternate Nostril Breath can be a great technique to calm the mind and balance your Nervous System. 
One round of Anuloma Viloma consists of six steps, shown below. Start by practicing five rounds and build up slowly to ten or more rounds. You could start with a ratio of 1:1 to 1:1:1. Once you feel comfortable with this you can practice a ratio of 1:1:2 to 1:2:2. It’s important for the practice to be as comfortable as possible and to not create tension. 
Alternate Nostril Breath should not be practiced if you have a cold, or your nasal passages are blocked. Forcing the breath through the nose can cause problems. Always follow this rule when practicing yoga and breathwork: under no circumstances should anything be forced. If your nasal passages are blocked practice visual Alternate Nostril breathing. This is where you see and/or sense the breath moving through the nostrils as if you were actually doing the physical practice. When practicing visual Alternate nostril breathing eliminate any counting or breath holds.
In Anuloma Viloma, you use a hand position with your right hand called Vishnu Mudra. You will use this hand position in the following way to control your breath by closing and opening alternate nostrils; tuck the index and middle finger of your right hand into your palm, place the thumb by your right nostril and the ring and pinky finger by your left nostril. 

One Round of Anuloma Viloma - Alternate Nostril Breath - 1:1:1 ratio

Placing the thumb on your right nostril inhale through the left nostril, to the count of four.
Hold the breath while you close both nostrils, to the count of four.
Close the left nostril with your ring and pinky finger and exhale through the right nostril, to the count of four.
Inhale through the right nostril, keeping the left nostril closed with the ring and pinky finger, to the count of four.
Hold the breath, closing both nostrils, to the count of four.
Exhale through the left nostril, keeping the right closed with the thumb, to the count of four.

Benefits of Anuloma Viloma
The breathing technique of Anuloma Viloma creates beautiful balance to both sides of our brain: beautiful creativity and beautiful logical verbal activity. So, both sides of our brain, the left side which is responsible for logical thinking and the right side which is responsible for creative thinking function equally beautiful.

Modern Scientist Confirms
The nasal cycle is something that yogis discovered thousands of years ago and is just recently being discovered by Medical science. What modern scientists found is that we do not breathe equally through both nostrils. Each nostril alternates about every three hours. The Yogis tell us that the natural period is every two hours, keep in mind scientific studies were done on people who are not particularly healthy. 
If you are really healthy, you will breathe predominantly through the Ida (left nostril) for around 2 hours, then switch to the Pingala (right nostril) for 2 hours. Because many of us are not in perfect health, this time period varies which greatly reduces our vitality. 
Scientists also discovered that the nasal cycle corresponds with brain function. The electrical activity of the brain was found to be greater on the side opposite the less congested nostril. The right side of the brain controls creative activity, while the left side controls logical verbal activity. The research showed that when the left nostril was less obstructed, the right side of the brain was predominant. Test subjects were indeed found to do better on creative tests. Similarly when the right nostril was less obstructed the left side of the brain was predominant. Test subjects did better on verbal skills. 
Medical science has not quite caught up with the ancient Yogis yet. The Ancient Yogis even went one step further. They observed that a lot of diseases were due to disturbances in the nasal cycle like if a person breathes for too long through one nostril. To prevent and correct this condition, they developed the Alternate Nostril Breathing Technique.