Context. We investigate the response of the heliosphere to fluctuations in the local interstellar medium (LISM) as compared to the influence of solar-cycle fluctuations. Aims. We discuss the differences between effects coming from the two types of drivers of time-dependent effects in the heliosphere in the context of the shape of the heliosphere, the thickness of the inner heliosheath, and the position of the ribbon of enhanced energetic neutral particle emission, as observed by the IBEX mission. Methods. Our study is based on a comparison of fully time-dependent simulations obtained with a three-dimensional (3D) model of the heliosphere. Results. We show that density fluctuations, taking the form of entropy waves and originating from the LISM, may reduce the thickness of the inner heliosheath to a similar extent as the solar-cycle effects. However, the relative motions of the termination shock and the heliopause in the two types of simulations are different. The amplitude of variation of the heliopause position is greater for the LISM fluctuation. The IBEX ribbon position is shown to be not significantly affected by the two types of drivers, although the effect of LISM fluctuation is stronger than that of the solar cycle. In this context, slight systematic changes of the position of the IBEX ribbon in its different sectors (i.e., changes in the heliospheric nose followed by variations in the heliospheric flanks) may serve as an indicator of the passage of a density fluctuation in the LISM, as suggested by our study. We also discuss the difficulties in fitting the LISM parameters in the presence of time-dependent effects.
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