Integer-dimensional fractals of nonlinear dynamics, control mechanisms, and physical implications.

ABSTRACT: 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 fix

SUBMITTER: He Z 

PROVIDER: S-EPMC6037749 | biostudies-literature | 2018 Jul

REPOSITORIES: biostudies-literature