在相互作用的社区中出现混乱
Emergence of chaos in interacting communities
摘要：
我们介绍了一个简单的动态模型，两个相互作用的社区，其元素受到随机离散时间更新，只有双线性相互作用。当内部耦合和相互耦合是合作的，两个社区达到渐近的平衡态。然而，当内部或相互耦合是反合作的，系统可能会保持在永久振荡，当耦合值属于一定的区间，出现两种可能的情况下，其特征在于由不稳定的非周期性轨迹和高灵敏度的耦合的小变化，或由混沌轨迹和分叉级联。有趣的是，我们发现，即使是一个单一社区的温和共识也可以消除混乱。模型与相互作用的股票市场的连接进行了讨论。
英文摘要：
We introduce a simple dynamical model of two interacting communities whose elements are subject to stochastic discrete-time updates governed by only bilinear interactions. When the intra- and inter-couplings are cooperative, the two communities reach asymptotically an equilibrium state. However, when the intra- or inter-couplings are anti-cooperative, the system may remain in perpetual oscillations and, when the coupling values belong to certain intervals, two possible scenarios arise, characterized either by erratic aperiodic trajectories and high sensitiveness to small changes of the couplings, or by chaotic trajectories and bifurcation cascades. Quite interestingly, we find out that even a moderate consensus in one single community can remove the chaos. Connections of the model with interacting stock markets are discussed.
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