Abstract
The co-evolutionary dynamics of a cyclic game system is investigated in a two-dimensional square lattice with the asymmetrical rates for three species. Different with the well-mixed system, coexistence and extinction emerge alternately in the system, where a “zero-one" behavior is robust for a small population size, whereas, the system is predominated by coexistence for a big population one. We study in detail the influence about the fluctuation to the change of the state, and find that the difference between the maximal amplitude about the fluctuation and the average intensity determines which state the system is ultimately. In addition, we introduce Potts energy to explain the reason of the “zero-one" behavior. It is shown that the average Potts energy per site is the distance to the “zero-one" behavior in the model.
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