AI 中文总结
该研究将记忆引入Lotka-Volterra模型，发现文化领域注意力竞争的无胜者混沌区域，其参数接近最大Lyapunov指数局部最大值，即文化竞争过程在记忆起关键作用时处于最大混沌状态。
AI 中文摘要
记忆是文化项目在竞争注意力进而竞争成功（如音乐榜单中的歌曲）时的关键决定因素。建模时，需将记忆加入Lotka-Volterra模型——马尔可夫竞争过程的参考模型。此处以指数移动平均处理记忆，发现其会产生无胜者混沌的扩展区域，该区域的特征是 trailing top-k榜单中呈现对数正态的流行度统计。重要的是，当反馈动态在榜单周期尺度上较快时，观测到的对数正态行为会坍缩为幂律分布，这一结果与现实世界音乐榜单（如Billboard和Spotify）的观测统计一致。在混沌状态下，最大Lyapunov指数的大小是系统不可预测性的度量。我们发现，在无胜者混沌稳定的相位中，最大Lyapunov指数随参数剧烈变化。有趣的是，通过将模拟结果与从Google Books、Google Trends、电影、Reddit、维基百科、Twitter及科学出版物中提取的现实世界文化项目动态对比得到的参数集，位于最大Lyapunov指数达到局部最大值的参数空间点附近，即接近最大不可预测性的点。该结果表明，当记忆是关键决定因素时，文化竞争过程处于最大混沌状态。
英文摘要
Memory is a key determinant when cultural items compete for attention and, consequently, for success, as in the case of songs on a music chart. For modeling, one adds memory to Lotka-Volterra models, the reference for Markovian competitive processes. Here we treat memory in terms of an exponential moving average, finding that it leads to an extended region of winnerless chaos characterized by log-normal popularity statistics in trailing top-k charts. Importantly, the observed log-normal behavior collapses to a power-law distribution when the feedback dynamics is fast on the scale of the charting period. This result is in agreement with the observed statistics of real-world music charts (e.g., Billboard and Spotify). In a chaotic state, the size of the largest Lyapunov exponent is a measure of how unpredictable the system is. We find that the largest Lyapunov exponent varies strongly as a function of parameters in the phase where winnerless chaos is stable. Interestingly, the sets of parameters obtained by comparing simulations with real-world cultural-item dynamics extracted from Google Books and Google Trends, movies, Reddit, Wikipedia, Twitter, and scientific publications, are located close to the points in parameter space where the largest Lyapunov exponent reaches its local maximum, namely, close to the point of maximal unpredictability. This result suggests that cultural competitive processes are maximally chaotic when memory is a key determinant.
Commentsmain paper: 16 pages, appendices: 8 pages, supplementary material: 13 pages
