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We discuss a mechanism that induces a time-dependent vacuum energy oncosmological scales. It is based on the instability induced renormalizationtriggered by the low energy quantum fluctuations in a Universe with a positivecosmological constant. We employ the dynamical systems approach to study thequalitative behavior of Friedmann-Robertson-Walker cosmologies where thecosmological constant is dynamically evolving according with thisnonperturbative scaling at low energies. It will be shown that it is possibleto realize a "two regimes" dark energy phases, where an unstable early phase ofpower-law evolution of the scale factor is followed by an accelerated expansionera at late times.

Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity