Long Memory Properties and Complex Systems
a complex environment and a simple environment , the present authors also modified the code to allow the removal of spatial complexity , by setting all patches identically and configuring the sugar restoration parameter to be larger than the agents ’ metabolism . Moreover , all heterogeneity between the patches is removed by imposing the same sugar capacity values for all of them — all patches having maximum capacity .
Consequently , in a first simulation , the system behaves like a stable intransient deterministic system .
After that , in a second simulation , the model is again modified , in order to generate spatial complexity . To achieve that , the sugar restoration and sugar capacity parameters are set to default values ( identical to the original model ), keeping all agents initially homogenous between themselves .
Furthermore , heterogeneity is imposed over the patches by setting different and random sugar capacities , where only 5 % of the patches have the maximum capacity .
Hence , this second configuration produces a result much similar to a stochastic process .
In order to check such results , a Gini coefficient time series was calculated over the food quantity that each agent has — in this case , sugar is the Wealth in this simple artificial economy , simulated over 2,000 periods .
Then , as can be seen in Figure 20 , in the first discussed modification the system rapidly converges towards a fixed point . However , in the second configuration , the system behaves like a stochastic process , producing long memory properties that are going to be discussed later .
Figure 20 . Evolution of simulated indexes .
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