Abstract
The objective of this research is to investigate the dynamical behavior of the Bianchi IX Universe through various inflationary models induced by scalar fields. Specifically, we explore potentials for the inflaton field of the form V(ϕ)∝ϕδ, where c varies from 1 to 4. To discern any chaotic behavior in the system, we calculate basin diagrams using the smaller alignment index (SALI) and the grid classification method. The fractal nature of the basins is evaluated through the utilization of two distinct indicators, namely the box-counting dimension and the boundary basin entropy. Our findings reveal that the inflaton affects the stability of the Bianchi IX model, which is intrinsically chaotic and becomes more stable as the power of the scalar-field potential increases. Moreover, except in the case δ=1, the impact of the scalar field on the dynamics is independent of the exponent δ.
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