Integer-dimensional fractals of nonlinear dynamics, control mechanisms, and physical implications
| Autor: | Zonglu He |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Multidisciplinary
Spacetime lcsh:R lcsh:Medicine Relative strength Fixed point 01 natural sciences Measure (mathematics) Article 03 medical and health sciences Nonlinear system 0302 clinical medicine Amplitude Fractal 0103 physical sciences lcsh:Q Statistical physics lcsh:Science 010306 general physics 030217 neurology & neurosurgery Integer (computer science) Mathematics |
| Zdroj: | Scientific Reports Scientific Reports, Vol 8, Iss 1, Pp 1-17 (2018) |
| ISSN: | 2045-2322 |
| DOI: | 10.1038/s41598-018-28669-3 |
| Popis: | Fractal dimensionality is accepted as a measure of complexity for systems that cannot be described by integer dimensions. However, fractal control mechanisms, physical implications, and relations to nonlinear dynamics have not yet been fully clarified. Herein we explore these issues in a spacetime using a nonlinear integrated model derived by applying Newton’s second law into self-regulating systems. We discover that (i) a stochastic stable fixed point exhibits self-similarity and long-term memory, while a deterministic stable fixed point usually only exhibits self-similarity, if our observation scale is large enough; (ii) stochastic/deterministic period cycles and chaos only exhibit long-term memory, but also self-similarity for even restorative delays; (iii) fractal level of a stable fixed point is controlled primarily by the wave indicators that reflect the relative strength of extrinsic to intrinsic forces: a larger absolute slope (smaller amplitude) indicator leads to higher positive dependence (self-similarity), and a relatively large amplitude indicator or an even restorative delay could make the dependence oscillate; and (iv) fractal levels of period cycles and chaos rely on the intrinsic resistance, restoration, and regulative delays. Our findings suggest that fractals of self-regulating systems can be measured by integer dimensions. |
| Databáze: | OpenAIRE |
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