期刊
ADVANCES IN COMPLEX SYSTEMS
卷 13, 期 3, 页码 327-338出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021952591000258X
关键词
Emergence; persistent mutual information; chaotic dynamical systems; complexity measure; logistic map
资金
- EPSRC, Warwick Complexity Science Doctoral Training Centre [EP/E501311/1]
- EPSRC [EP/E501311/1] Funding Source: UKRI
We define Persistent Mutual Information (PMI) as the Mutual (Shannon) Information between the past history of a system and its evolution significantly later in the future. This quantifies how much past observations enable long-term prediction, which we propose as the primary signature of (Strong) Emergent Behavior. The key feature of our definition of PMI is the omission of an interval of present time, so that the mutual information between close times is excluded: this renders PMI robust to superposed noise or chaotic behavior or graininess of data, distinguishing it from a range of established Complexity Measures. For the logistic map, we compare predicted with measured long-time PMI data. We show that measured PMI data captures not just the period doubling cascade but also the associated cascade of banded chaos, without confusion by the overlayer of chaotic decoration. We find that the standard map has apparently infinite PMI, but with well-defined fractal scaling which we can interpret in terms of the relative information codimension. Whilst our main focus is in terms of PMI over time, we can also apply the idea to PMI across space in spatially-extended systems as a generalization of the notion of ordered phases.
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