Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2015-10-01

Journal: NONLINEAR DYNAMICS

Included Journals: Scopus、SCIE、EI

Volume: 82

Issue: 1-2

Page Number: 143-156

ISSN: 0924-090X

Key Words: Generalized M sets; Generalized J sets; Noise perturbations; Quaternion; Fractal

Abstract: In this study, the quaternion Mandelbrot sets and Julia sets (abbreviated as M-J sets) with additive and multiplicative noise perturbations are constructed and the changes of their fractal characteristics are explored. The experimental results show that the quaternion M sets with additive noise perturbations move in the direction of the noise, while the structures remain unchanged. The quaternion J sets with additive noise perturbations change dramatically both in the structures and in the periodicities. The quaternion M sets with multiplicative noise perturbations present scaling and rotation, while the stable regions maintain the same distributions as the non-perturbed M sets. The structures and the periodicities of the J sets change under multiplicative noise perturbations, keeping different sensitivity to the noise parameters. The M sets and J sets still share the same stable points under both the additive and multiplicative noise perturbations.