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This work explores the dynamical stability of cosmological models where darkmatter and dark energy can non-minimally couple to spacetime (scalar)curvature. Two different scenarios are presented here. In the initial case,only dark matter sector is coupled to curvature in the presence of aquintessence scalar field. In the second case both dark matter and thequintessence field are coupled to curvature. It is shown that one can get anaccelerating expansion phase of the universe in both the cases. The nature ofthe fixed points show that there can be stable or unstable phases where thecurvature coupling vanishes and dark energy and dark matter evolveindependently. On the other hand there can be stable accelerating expansionphases where both the components are coupled to curvature.

Dynamical stability in models where dark matter and dark energy are non-minimally coupled to curvature