A typical example of this last mentioned case is the interval between the 1st and 2nd Empire of Thebes (approx. 1,700 years B.C.) in the Egyptian culture. Likewise, the interval between the Han Dynasty or Mongolian Empire (approx. 200 years B.C.). When the empire is in its second cycle, that is, when the cycle of 1,700 years is about to end, then the nation begins the phase of great demographic fractionation, as in the case of the Byzantine Empire, disintegrated in a large number of small kingdoms, and as will be the case of the present Muscovite Empire, where the Slavic Nations will undergo an evolution towards the great era of great demographic fractionation.
As an example of the process of a nucleus we present the case of Rome in its first period of great strategic victories (270-139 B.C.), with the second Punic war it defeats Carthage. This Empire is founded in the year 879 B.C. and had undergone its period of great strategic victories (beginning of the VII Century up to 349 B.C.). Carthage, now in its first Punic war, manifested the spirit of indifference of the Carthaginians and of the Senate. In the year 382, it was full of the spirit of domination (the first period of Great Strategic Victories), in the year 255 it shows to be completely indifferent up to the extreme of abandoning its fleet. Thus, in spite of it all and having great Generals at its disposal, it had a defeat at Mylae in the year 260.
Afterwards there were new military losses until there was total ruin. The Empire was leaving the great depression when Hamilcar reorganizes the army and begins the conquests to thus enter its second period of great strategic victories, which arrives with Hannibal at his best. Immediately following comes the conquest of Italy (218).
It should be noted that Carthage had already gone through a long period in the first of great victories, and in these cases the second period of great triumphs, conservation and disintegration, are short in order to compensate the time of duration of the empire and, in this manner arrive at its end of approximately five and one-half centuries, with a very logical precipitation. Furthermore, Carthage had not had a military disaster. On its part, Rome presented itself thus: first Punic War (264-241), it conquers Sicily, Corsica and Sardinia. The first Roman-Macedonian War (221-205), where Macedonia is defeated. The time and its characteristics in victory, classified it in the first period of great strategic victories.
To summarize: Carthage launched itself into an offensive war with Hannibal, but with an already advanced Empire reaching its end and without a military disaster. It was about to confront another empire of lesser prestige at that time, but with youth and in its first period of great strategic victories. The Italian campaign by Hannibal begins with his triumphs in the battles of Mount Tesina, Trebbia, Trasimene and Cannae, returning to Carthage where he is defeated in Zama by Scipio.
Studying the enemy from the point of view of the mathematical-historical concept, is then, a new factor of the decision that should be analyzed and that completely influences the results in war.
The Macedonian Empire, constituted in the year 750 B.C., ends its first period of great strategic victories in the year 506, with the kingdom of Amintas I, after the great depression (506-413). This Empire is defeated by the Persian Empire. In the second period of great strategic victories (413-323), the Athenians are defeated and the Ionian colonies go on to become part of the Macedonian power. In the year 338 the dominion over Greece is complete.
Under the leadership of Alexander the Great (334-325) in the second period, the Macedonian Empire reaches its maximum point. In the year 221, Phillip the III, confronts the Roman Empire. The latter formed in 270, had its first victory in the first Punic War.
As a summary: Phillip the III with his Empire in its stage of disintegration, against the Roman Empire in its first period, which destroys the Macedonian fleet. The war begins again in the year 211 and is prolonged until 205 B.C., when Phillip made peace in Rome. In the space of time 200-197, Phillip is conquered in Cynoscephalae. The third Roman-Macedonian War ends the Macedonian Empire, which is totally absorbed by Rome in 146.