Confronting dark energy models mimicking $\Lambda$CDM epoch with
  observational constraints: future cosmological perturbations decay or future
  Rip?
  We confront dark energy models which are currently similar to $\Lambda$CDM
theory with observational data which include the SNe data, matter density
perturbations and baryon acoustic oscillations data. DE cosmology under
consideration may evolve to Big Rip, type II or type III future singularity, or
to Little Rip or Pseudo-Rip universe. It is shown that matter perturbations
data define more precisely the possible deviation from $\Lambda$CDM model than
consideration of SNe data only. The combined data analysis proves that DE
models under consideration are as consistent as $\Lambda$CDM model. We
demonstrate that growth of matter density perturbations may occur at
sufficiently small background density but still before the possible
disintegration of bound objects (like clusters of galaxies, galaxies, etc) in
Big Rip, type III singularity, Little Rip or Pseudo-Rip universe. This new
effect may bring the future universe to chaotic state well before
disintegration or Rip.
