Phase-Plane Analysis of FRW Cosmological Model with Variable A in Lyra Geometry

The present work deals with the dynamical evolution of Friedmann-Robertson-Walker (FRW) Cosmologies with variable A in Lyra geometry. We perform phase-plane analysis of the model with a time-dependent displacement vector, considering a variable A, i.e., A proportional to beta(2) for model I and A proportional to H-3 for model II. To analyze the evolution equations, we introduce a suitable transformation of variables. The results are presented by curves in the phase-plane diagram. The nature of critical points is analyzed, and stable attractors are examined for both cosmological models. We determine the classical stability of these cosmologies. We also examine the transition of an early decelerated stage of the Universe to the present accelerated stage for both models.