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Multiacceleration scenario can be used to solve the cosmological coincidenceproblem. In this paper, after considering the early radiation era, we revisitthe cosmological dynamics of the oscillating dark energy model proposed in[https://doi.org/10.1103/PhysRevD.101.063531, Phys. Rev. D {\bf 101}, 063531(2020)]. We find this model allows the Universe evolves as oscillating scalingsolution (OSS) in the radiation era and as chaotic accelerating solution (CAS)in the matter era. Mathematically, the transition from OSS to CAS is a route ofperiod-doubling bifurcation to chaos. Physically, there are two reasonsconvince us that this scenario can be a nice picture to describe the realUniverse. One is the global cosmological parameter constraints are practicableif the Universe evolves as OSS in the radiation era. The other is the late-timeUniverse described by CAS can successfully explain the observed cosmicacceleration at low redshifts.

Cosmological consequences of a scalar field with oscillating equation of state. II. Oscillating scaling and chaotic accelerating solutions