Dynamical System Study of Nonminimal Tachyon Field within Holographic Cosmology

We use the dynamical system method in order to investigate the dynamics of a non-minimally coupled tachyon field within induced gravity on the brane in a holographic cosmological context. Assuming an exponential potential and a monomial form of the nonminimal coupling function, we construct the phase space of the model. Two possible cases, namely, the minimal and nonminimal coupling, are investigated. Using dynamical systems tools, it is found that the model can describe an attractor solution which corresponds to the inflationary era in the non-minimal coupling case.