Lamb-lion Problem on Networks and Its Applications

We numerically study the dynamic properties of diffusing lamb captured by diffusing lion on the complex networks. We find that the survival probability $S(t)$ of a lamb decays exponentially on the complex networks including scale-free networks whose degree distribution follows $P(k) \sim k^{- \gamma}$. We also find that the average life time $$ depends on the size of the underlying networks, $N$, and it satisfies the relation $ \sim N^{\alpha}$ for $\gamma > 3$. However, for small values of $\gamma$ ($<3$) we find that $$ does not follow the power-law. Finally, we investigate the topological property of the node at which the lion captures the lamb by measuring the degree of the node. We also discuss some possible applications of our findings.