基于沙堆模型的国家动力学研究--以中国历史为例(前221年到1912年)

关于帝国兴衰,长期存在的“超稳定结构”理论并不能呈现动态的历史过程。复杂性学科的“自组织临界性”理论,能够模拟帝国兴衰的动态过程,并对“超稳定结构说”形成补充。自然系统(沙堆模型)与社会系统类似,都在自动、自发地趋近临界状态,我们可以通过社会计算模型揭示帝国兴衰的动力学机制。研究目标,是精准拟合中国大历史,即秦汉到明清的2132年的农业帝国兴衰演变史,包括朝代数量、朝代寿命等客观指标,使用具体智能体ABM模型,建构代表帝国社会有机体的沙堆模型。通过参数遍历仿真,求解最优的参数解。基于最优解,重复模拟1000次,求取均值获得稳健性结果。研究表明:第一,沙堆模型具有拟合有效性。中国历史上有22个朝代,沙堆模型可以“涌现”相同数量的朝代或帝国,而且数量遵循正态分布(平均值是22)。第二,沙堆模型具有重复稳健性。朝代寿命遵循幂律分布,模拟结果与真实历史呈现高度吻合。第三,沙堆模型具有可推广性。同样可以刻画非22帝国情况。22朝代是公认标准,但历史存在非线性、偶然性。因此需要拟合数量不等于22的情况。舍弃历史上1~3个短寿朝代,构建19、20、21组历史与仿真朝代队列,依然实现高精确度拟合。在23、24、25个仿真朝代中,舍弃1~3个短寿者,构成22组历史与仿真朝代,拟合度同样良好。沙堆模型对帝国兴衰历史、当前中美大国博弈,具有借鉴与指导意义。

According to the self-organized criticality theory,the sandpile model is built to investigate the evolutionary dynamics of empires in the history of China.The methods of agent-based modeling and simulations are applied to capture empires'mechanism of rising and falling cycles,and to obtain the observed life cycle pattern of empires in history.Under the self-organized criticality theory,natural systems and human empires systems have similar structures and mechanisms,which makes systems reach the critical states automatically.Therefore,the rising and falling dynamics of empires can be reflected by the sandpile model as well.With the sandpile modeling and simulations,the optimal solution of parameters can be found,based on which the satisfactory fitness of results can be achieved.Under the optimal solution,we run the simulations for 1000 times to check the fitness and robustness.First,the number of empires can be matched.There were 22 empires in the history of China,and the same number of empires can be obtained via sandpile model simulations,and the amount of empires follows the normal distribution with the mean of 22 empires.Second,the distribution of empire durations follows the power-law distribution,for both simulated and historical empires.Third,for less than 22 simulated empires,we drop empires with tiny durations in history to compare the 19,20,and 21 pairs of counterparts respectively,and the fitness can be guaranteed as well.Finally,for more than 22 empires,we drop simulated empires with tiny durations to compare the 23,24,and 25 pairs,the matching degree is satisfactory as well.It indicates that multiple simulations have more robust and stable outcomes than one,even the best,simulation.