Born-Infeld Type Phantom Model in the $\omega -{\omega }^{\prime }$ Plane

Abstract

In this paper, we investigate the dynamics of Born-Infeld(B-I) phantom model in the $\omega -{\omega }^{\prime }$ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to $N$(the logarithm of the scale factor $a$). We find the scalar field equation of motion in $\omega -{\omega }^{\prime }$ plane, and show mathematically the property of attractor solutions which correspond to ${\omega }_{\varphi }\sim -1$, ${\Omega }_{\varphi }=1$, which avoid the "Big rip" problem and meets the current observations well.

6 pages, 3 figures, some references added

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