Rand D A, Wilson H B
Arbeitsgruppe Theoretische Okologie, Forschungszentrum Jülich, F.R.G.
Proc Biol Sci. 1991 Nov 22;246(1316):179-84. doi: 10.1098/rspb.1991.0142.
We address the question of whether or not childhood epidemics such as measles and chickenpox are chaotic, and argue that the best explanation of the observed unpredictability is that it is a manifestation of what we call chaotic stochasticity. Such chaos is driven and made permanent by the fluctuations from the mean field encountered in epidemics, or by extrinsic stochastic noise, and is dependent upon the existence of chaotic repellors in the mean field dynamics. Its existence is also a consequence of the near extinctions in the epidemic. For such systems, chaotic stochasticity is likely to be far more ubiquitous than the presence of deterministic chaotic attractors. It is likely to be a common phenomenon in biological dynamics.
我们探讨了诸如麻疹和水痘等儿童期流行病是否具有混沌性这一问题，并认为对所观察到的不可预测性的最佳解释是，它是我们所称的混沌随机性的一种表现。这种混沌是由流行病中平均场的波动或外在随机噪声驱动并使其持久存在的，并且依赖于平均场动力学中混沌排斥子的存在。它的存在也是流行病中近乎灭绝的结果。对于此类系统，混沌随机性可能比确定性混沌吸引子的存在更为普遍。它很可能是生物动力学中的一种常见现象。
