<![CDATA[In ancient China there are three model of society which is farmers, bandits and ruler. When the authority (rulers) is not there, the dynamics system of farmers and bandits become predator-prey interactions system. In here rulers play role on taxing the farmers and catching the bandits and then punish them. Thus, farmers are a sort of renewable resource which is exploited both by bandits and by rulers. In this paper, optimal control is applied to reduce the bandit’s population, by reducing it, the ruler population can also be reduced because the existing bandits can be conquered, so that the cost of running a government is more efficient because it can reduce the need for eradicating bandits from ruler. The type of the optimal control here is fixed time and free end point.]]>
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