Not a variable star with fluctuating brightness, but our sun is getting brighter gradually over time. As the fuel in the sun is spent the sun gets 10% brighter and 10% hotter every billion years. So we estimate in a couple billion or so years the oceans will dry up and all life on Earth will cease. Earth will become much like Venus is now. Eventually the sun will turn into a red giant and expand to swallow Mercury, Venus and probably Earth.