There was a very good article that was found at this link 
http://www.vetmed.auburn.edu/sac/mededu/diabetes/somogyi.html
which seems to not be working at this time so here is the page 
that was originally found there.
 

Somogyi

Below is a blood glucose curve depicting the Somogyi phenomenon. In this scenario,
the positive urine glucoses prompted continued escalation in the insulin dose administered.
The subsequent insulin toxicity (and concomitant hypoglycemia –or low blood glucose) resulted in 
initiation of protective compensatory mechanisms which caused massive transient rises in blood sugar.

In this case, urine dipsticks for glucose were checked twice daily and were always positive, prompting 
the owners to incrementally increase the insulin dose. This graph depicts in days what usually happens 
over weeks when well-meaning concerned pet owners try to use urine dipsticks to determine insulin
dosing. Fortunately, the body is able to release several hormones which increase the amount of 
circulating glucose and which “shield” the tissues from the effects of insulin. Over time, even as the body
is experiencing dramatic fluctuations in blood sugar levels, the tissues develop a resistance to insulin which 
may require weeks of insulin withdrawal to resolve. The best way to avoid Somogyi is to base insulin dose
adjustments on blood, not urine glucose levels. Your veterinarian can do this by using a glucometer with just 
a drop of blood acquired every 2-3 hours for 12-24 hours, depending on how often insulin is administered.

Somogyi effect: A condition in which the blood glucose level increases if too much insulin is given. 
It occurs when insulin causes the blood glucose level to go so low it stimulates the production of 
other hormones in the body such as epinephrine which promote the breakdown of glycogen (
the chemical compound which the body uses to store glucose) and increases the blood glucose 
level above normal. It is also called rebound hyperglycemia or insulin-induced hyperglycemia.

In case the insulin dose is slightly too high, the Somogyi - effect may 
occur.  This is a chain reaction of the body to a sluggish decline of the 
blood glucose leve.  If after insulin injection the glucose level has 
decreased to approx. 3 mmol/l, the patient will become hungry and restless 
or lethargic.  Due to a decling glucose level in the CNS, adrenaline and 
subsequently cortisol, glucagon and growth hormone will be released.  These 
hormones will induce an increase of the blood glucose level(through 
gluconeogenesis, release of glucose from hepatic glycogen and increase in 
the peripheral resistance to insulin).  This results in a rapid rise of the 
glucose level shortly after the second meal.  During the rest of the 24 
hour period, the blood glucose level further increases to 15-18 mmol/l or 
even higher.  The urine glucose level is negative during the day, but rises 
in the evening and night and will become strongly positive in the morning. 
Symptoms of polyuria and polydipsia will occur.  This condition bears the 
risk that if guided only by the results of urine tests, the insulin dose 
will be increased.  This is absolutely contraindicated since in this way a 
severe hypoglycemia will be induced.  In contrast, the insulin dose must be 
decreased by 20%! 

The reason: Anytime the glucose level drops too far or too fast, the cat or dog may defensively dump glucose (converted from glycogen in the liver), as well as hormones epinephrine and cortisol, into the bloodstream. (If these are insufficient, hypoglycemia ensues!) The glycogen raises the blood glucose, the other two may make the pet insulin-resistant for a time. This phenomenon was first documented by a Dr. Somogyi.[17] [18].

Even when raising the insulin dose slowly and carefully, it's possible to pass the correct dose and go on to an overdose. (A typical case is increasing bidaily dosage from 1 unit to 2, passing a correct dose of 1.5 units.) This may produce a rebound -- a swift jump in blood glucose up from a dangerously low reading, to beyond the previous pre-shot level. The pet may be a bit less responsive to the same dose the next shot, from those other hormones. Repeating the overdose on subsequent days, and checking only pre-shot readings or urine glucose, can give the dangerously wrong impression that more insulin is needed! Remember to check occasionally at the expected nadir (low point) as well.

It's unusual to be monitoring glucose right when this happens, and typical to just continue the overdose, leading to a repeated rebound situation. So it's good to learn to recognize the patterns of repeated rebound.

A typical rebound pattern, most often seen with long-acting insulins, is a high, flat, unresponsive blood sugar over a period of days. Sometimes, often when raising dosage, this high flat curve will be punctuated by sudden drops to very low values, (with possible hypoglycemic events) followed by a fast return to high unresponsive numbers. (It's the sudden dip that distinguishes this pattern from inadequate insulin!) 
When using shorter-acting insulins, repeated Somogyi rebound may manifest instead as rapidly alternating high and low blood sugar numbers with no apparent logic. The highs and lows will both be exaggerated compared to what you'd see on a smaller dose. 
It's not always easy to tell a rebound from a regular curve showing insulin action ending normally. One way to tell the difference is to take a "curve" (repeated tests every 2 hours starting with the insulin shot) on a weekend and look for the shape of the curve. If the curve is valley-shaped, and gradual, then you are not seeing Somogyi rebound. Other shapes should arouse suspicion. In particular, if the rise after peak action is faster and rises higher than the original pre-insulin level and the original fall in blood sugar, you have good cause to consider rebound. The only sure way to check is to reduce dosage and look for a better-shaped curve.

A fairly sure sign: Anytime blood glucose numbers seem higher after dosage is raised, consider the possibility of a somogyi rebound. But other things can cause unexpectedly high blood glucose too, so look for a clear correlation with dosage changes.

This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.

Offsite Explanation
www.petdiabetes.org has a very good page on somogyi phenomenon

 http://www.petdiabetes.org/somogyi.htm

.
This page was updated on July 5, 2006