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The extended holographic dark energy model with the Hubble horizon as theinfrared cutoff avoids the problem of the circular reasoning of the holographicdark energy model. Unfortunately, it is hit with the no-go theorem. In thispaper, we consider the extended holographic dark energy model with a potential,$V(\phi)$, for the Brans-Dicke scalar field. With the addition of a potentialfor the Brans-Dicke scalar field, the extended holographic dark energy modelusing the Hubble horizon as the infrared cutoff is a viable dark energy model,and the model has the dark energy dominated attractor solution.

The dynamical behavior of the Extended Holographic Dark Energy with Hubble Horizon