We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity ($\delta$) and fibroblast density ($\eta$) affect the stability of the myocardial tissue. We provide mathematical and computational arguments indicating that there is a region of instability in the $\eta-\delta$ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D,2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts.