Generally speaking, empires don't undergo these phases of existence, at least not in such concrete terms. As Hayden White put it in the introduction to Metahistory, we as humans have an innate desire to impose order upon the past. Thus we tend to view history in the terms of a story, or a series of stories, with a beginning, middle, and end. We shape the 'facts' of history into a concrete narrative structure in order to give it meaning. In our stories about history empires rise and fall in recognizable patterns, but that's just a result of how we have chosen to look at the past, and is far from being the only possibility.

For instance, in the past 30 years a lot of ink has been spilled over the problem of the application of the concept of 'decline' to Ottoman history. Originally, the idea was that after reaching a peak under the reign of the emperor Suleiman the Magnificent (r. 1520-1566), the Ottomans entered a slow decline from which they were unable to recover, gradually weakening and becoming eclipsed by Europe before finally being put out of their misery during World War I. Historians have now come to see an infinity of problems with this idea, but the most significant criticism for us here is that it's teleological - if we imagine the empire's history as the story of decline, it means judging the events of the 17th, 18th, and 19th centuries in light of the fact that the empire came to an end in the 20th. Placing the concept of 'decline' at the center of the empire's history meant ignoring everything which wasn't pointing toward that final outcome, the empire's dissolution. It meant ignoring whatever was really relevant for those middle years of the empire's history in a vain effort to answer the question of why the empire fell... hundreds and hundreds of years later.

I think 'decline', in the general sense of 'the decline of an entire empire' is a useless concept for discussing history because it leads one to be blinded by the empire's ultimate fate. Imagine for a moment that the EU will cease to exist in the year 2030 - would it make sense for historians writing the history of the EU to characterize its current state as being 'in decline', and emphasize everything which was unsuccessful about it just because at some later date it's going to stop existing? What matters for understanding any historical reality in any historical period is what was going on at the time, not what was destined to happen in the future. As far as I'm concerned, "Rise - Peak - Decline - Fall" paradigms are storytelling, not proper history.

On Ottoman decline: "Introduction: The Myth of Decline" in Darling, Linda. Revenue Raising and Legitimacy: Tax Collection and Finance Administration in the Ottoman Empire, 1560–1660. Leiden: E.J. Brill, 1996.