In 2022, the Event Horizon Telescope (EHT) collaboration has reported the first observations of Sagittarius A*(SgrA*). Applying the EHT observational results, we find out constraints on non-singular Hayward parameter of regular dark energy black hole. Considering these constraints and different thin disk accretion, we present a detailed investigation into influence of different dark energy and Hayward parameters on shadows from non-singular Hayward black holes. In the first second-order attenuation function model, corresponding shadow radius and peak for observed intensity from direct image decrease with increasing dark energy parameter and Hayward parameter. However, for the lensing ring and photon ring, corresponding peak become bigger as dark energy parameter increase in case of fixed Hayward parameter. In the second third-order attenuation function model, significantly different from model 1, above two rings completely overlay on the direct image, resulting in two distinct peaks in the observed intensity. As increase of Hayward and dark energy parameters, the difference between the two peaks decreases, and shadows and observed intensity decrease. In the final inverse trigonometric function attenuation model, the result shows corresponding lensing ring as well as photon ring can be distinguished within the superposition region, and the superposition region becomes larger. With the increase of the dark energy parameter, the shadow radius exhibits a decreasing trend, while observed intensity increases. However, with the increase of the Hayward parameter, both decreases. Compared with the first two models, the shadow radius becomes smaller, but the observed intensity becomes larger, making the bright ring wider and brighter. Therefore, different accretion models and non-singular Hayward parameters can give rise to interesting and distinguish characteristic for the black hole shadow and rings.
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