Simulating rise and fall cycles of Vietnam empires.

The life cycle pattern of empires is pervasive worldwide, and this is caused by multiple factors. In the history of Vietnam, there are totally about ten empires or dynasties, which have aggregately lasted for more than one thousand years. Here, we apply the life cycle model and agent-based modeling to uncover the underlying mechanisms of the life cycle pattern for Vietnam empires. Macroscopically, the man-land relationship greatly shapes the life cycle pattern of traditional agricultural empires. The balancing process between land and population is critical for the empires. The relationship between incomes and costs has determined the actions or strategies of the social members or individuals. It suggests that our optimal solutions and simulations have perfectly matched the real history of Vietnam. Under three optimal solutions, the distributions of simulated and real empire durations in history can be well-matched, in terms of both discrete (histogram) and continuous forms (kernel density). It indicates that the history of human society is a dynamic process, which is determined by certain evolutionary rules and regulations. Therefore, we are able to back-calculate, simulate, and even predict the future of empires or countries.