Abstract
We the authors want to further mention that the three fluid cosmological model has been considered before in some earlier works.
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1 Addendum to: Eur. Phys. J. C (2019) 79:362 https://doi.org/10.1140/epjc/s10052-019-6875-4
We the authors want to further mention that the three fluid cosmological model has been considered before in some earlier works. Especially in [1], to determine the viable nature of the scalar field potential, the authors applied an extra Lie symmetry to the dynamical system describing the model to conclude that the scalar field potential should be exponential. This is in accordance with our assumption. In [2], the author applied the Liyapunov methods to construct the Liyapunov functions in some of the non-hyperbolic cases to demonstrate the stability of the non-hyperbolic critical points. In contrast, in our paper we used the Center Manifold Theory to construct the center manifolds and the reduced systems to all the non-hyperbolic cases to demonstrate the stability. Although both the papers deal with essentially the same model, the methods incorporated are entirely different in their own merit.
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is an addendum of our original article. This addendum does not contain any data as it doesn’t need to but the original article contains all the data relevant to our research.]
References
M. Tsamparlis, A. Paliathanasis, Three fluid cosmological model using Lie and Noether symmetries. Class. Quant. Grav. 29(1) (2011). arXiv:1111.5567 [astro-ph]
M. Azreg-Aïnou, Phase-space analysis of the cosmological 3-fluid problem: families of attractors and repellers. Class. Quant. Grav. 30, 205001 (2013). arXiv:1304.7470v3 [astro-ph]
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The original article can be found online at https://doi.org/10.1140/epjc/s10052-019-6875-4.
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Pal, S., Chakraborty, S. Addendum to: Dynamical system analysis of a three fluid cosmological model: an invariant manifold approach. Eur. Phys. J. C 80, 457 (2020). https://doi.org/10.1140/epjc/s10052-020-7903-0
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DOI: https://doi.org/10.1140/epjc/s10052-020-7903-0