In my humble opinion, DO, a good analogy is what happened in Spain from the 9th century to the 13th — the Ummayads got soft (they still persecuted Christians and Jews, but were lazy about it) and were replaced by the fanatical Almoravids. Then, 4 generations later, the Almoravids were also lax in killing Jews and Christians and were replaced by the Almohads. These last were the most virulent and they initially won many battles against the Spainish reconquista before becoming so vile that they lost in the 1300s to Castile and Leon
I believe I get your point. You may be on track on that.
From a British General : http://www.telegraph.co.uk/news/worldnews/middleeast/iraq/11140860/Qatar-and-Saudi-Arabia-have-ignited-time-bomb-by-funding-global-spread-of-radical-Islam.html