In this paper, we deal with a Finsler–Randers (FR) cosmology in the framework of particle creation mechanism. The cosmological history of the model is studied by finding all the critical points and analysing their local stability.We study the behaviour of all critical points of the model when they are non-hyperbolic in nature using the centre manifold theory. The perseverance of the equilibrium points are illustrated by showing the vector field locally near the equilibrium point. The possible bifurcation scenarios are discussed in detail with the help of local bifurcation diagrams for each of the critical points. Concluding remarks and the cosmological upshot are also given.

In this paper, we deal with locally rotationally symmetric Bianchi type-$I$cosmological model with varying cosmological constant. Here, we have considered two models. In Model $I$, we have analysed total linear stability analysis for linear coupling between the dark sector of the Universe where as in Model $II$, the quadratic coupling between the dark sector of the Universe is considered. The cosmological history of the models is studied by finding all the critical points and analysing their local stability. We study the behaviour of all the critical points of the model when they are hyperbolic in nature using the linear Jacobi stability analysis and when they are non hyperbolic in nature using centre manifold theory. The perseverance of the equilibrium points is illustrated in phase portraits.