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Qualitative study of Bianchi type-I, III and Kantowski–Sachs cosmological models with scalar field

Raghavendra Chaubey

Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, India

E-mail Address: yahoo_raghav@rediffmail.com

E-mail Address: rchaubey@bhu.ac.in

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and

Rakesh Raushan

Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, India

E-mail Address: rakeshraushanjha@gmail.com

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https://doi.org/10.1142/S0219887816501231Cited by:14 (Source: Crossref)

Abstract

A qualitative analysis of Bianchi type-I, III and Kantowski–Sachs (KS) cosmological models with a scalar field and matter fluid is performed. The analysis of the resulting equations is made by the dynamical system method. To analyze the evolution equations, we have introduced suitable transformation of variables. The evolution of the corresponding solutions is represented by curves in the phase-plane diagram. We analyze the evolution of the effective equation of state parameter for Bianchi type-I, III and KS cosmological models. The nature of critical points are analyzed and stable attractors are examined for each cosmological model.

Keywords:

AMSC: 83F05, 83C05, 37N20

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