Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology

Abstract

Using the dynamical system theory we show that the Friedmann–Robertson–Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov–Takens normal form. The equation of state parameter, ω, the bulk viscosity coefficient, ξ, and the cosmological constant, Λ , define the necessary parameters for unfolding the degenerate Bogdanov-Takens system. The fixed points of the system are discussed together with the variation of their stability properties upon changing the relevant parameters ω, Λ and ξ. The variation of the stability properties are visualized by the appropriate bifurcation diagrams. Phase portrait for finite domain and global phase portrait are displayed and the issue of the structural stability is discussed. Typical issues such as late acceleration or inflation that can be induced by viscosity and could have relevance to observational cosmology are also discussed.