1 Introduction

The late stages of stellar evolution are characterized by regular and irregular light variability, a well-known signature of the stellar pulsation of Asymptotic Giant Branch stars (hereafter AGB). These light changes allow to identify AGB stars over large distances and to derive the pulsation characteristics (periodicity, etc.), which are key parameters for understanding the fundamental properties of the highly extended atmospheres of these stars. The pulsational properties have a strong impact on the structure of AGB stars. Pulsation, as the driving mechanism for the stellar winds, plays a key role for the high mass loss rates reached during the AGB phase.

A new era in the study of variable red giants started, when microlensing surveys produced a large amount of light curves of these stars, especially for objects in the LMC. The pioneering work by Wood (2000), using data from the MACHO survey, showed that the red giant variables form four roughly parallel sequences in a period-magnitude diagram. Three of these sequences could be associated with fundamental, first and second overtone pulsation. The explanation of the fourth sequence is not clear yet (Wood 2000; Hinkle et al. 2002). Recently, Cioni et al. (2001) presented a survey of variable red giants in the LMC based on data from the EROS-2 microlensing survey (Lasserre et al. 2000). The work of Cioni et al. focused on the $\log P-K$ relation confirming three of the relations found by Wood, and they discussed the behaviour of different groups of variables in near infrared colour-magnitude diagrams.

The present paper relies on the variability information contained in the AGAPEROS variable star catalogue (Melchior et al. 2000). Here, we extend and analyse the corresponding light curves, relying on the EROS-1 microlensing survey data set (Ansari et al. 1995; Aubourg et al. 1995). These data have been obtained between December 1991 and April 1994. The second half of the data set therefore overlaps with the MACHO survey. We combine the EROS data with $IJK_{\rm S}$ photometry of the DENIS survey (Epchtein et al. 1997), with an approach similar to the work of Cioni et al. (2001). The intention of our work is to discuss the light change of red variables on a large and homogeneous sample and to compare the results for LMC red variables with the corresponding objects in the Galactic Disk and Bulge.