Probing the dynamical system and thermal behaviors of the model, Λ0+3βH2

In this work we study the cosmological evolution of a two component model with non-relativistic dark matter and decaying vacuum of the form Λ = Λ 0 + 3 β H 2 . We contrast the model with the supernovae data and found that the model parameter β = − 0.010 when the interaction parameter, b = 0 and is β = − 0.002 when b = 0.001 . The thermal evolution study of the model indicates that it obeys the generalized second of entropy and also satisfies the convexity condition, S ¨ < 0 so that the model behaves like an ordinary macroscopic system which approaching a stable equilibrium thermal state at asymptotic conditions. The dynamical system analysis reveals that, the model posses a prior decelerated epoch represented by a saddle critical point and the late critical point represents an accelerating epoch which posses a convergence of phase-space trajectories from both the regions of the point hence can be considered as stable.