Suppose the energy generation rate at the center of a star were to
become
slightly smaller than its equilibrium value.  How would the star
regain its state of equilibrium?

"As the hydrogen is used up and the star's temperature cools slightly,
the outward force of energy starts to decrease, and as a result, the
star begins to implode under it's own gravitational force, which cause
the internal pressure and heat to increase again. Other heavier
elements, such as helium, are then fused to maintain the star's
equilibrium. In this stage of a stars life it will expand and contract
over millions of years before the actual Super Nova event occurs."

http://earths-trek.thexvector.com/science/crabneb.html "Constellation
Taurus: The Crab Nebulae" Earths Trek

"The nuclear reaction rate is very sensitive to temperature so that
even a slight increase in temperature makes the nuclear reactions
occur at a MUCH higher rate."

http://www.astronomynotes.com/starsun/s8.htm#A5.5 "Mass-Luminosity
Relation Explained" by Nick Strobel

"A star's equilibrium during the main-sequence phase is the result of
a balance between gravity and pressure, in which pressure's outward
push exactly counteracts gravity's inward pull...."

http://astronomy.nju.edu.cn/astron/AT3/AT32001.HTM "Leaving the Main
Sequence"

So, when the star's energy output becomes slightly smaller than its
equilibrium value, the star begins to implode, leading to increased
temperature.  The increased temperature causes a much higher rate of
nuclear reaction, which causes the star to expand again.  This leads
to a slower rate of reaction, so the star oscillates about a state of
equilibrium.

Sincerely,

Wonko

Excellent - the answers just keep getting better and better! Thank You!