  We consider the stochastic phase models for the community effect of cardiac
muscle cells. The model is the extension of the stochastic integrate-and-fire
model in which we incorporate the irreversibility after beating, induced
beating and refractory. We focus on investigating the expectation and variance
of (synchronized) beating interval. In particular, for the single-isolated
cell, we obtain the closed-form expectation and variance of the beating
interval, and we discover that the coefficient of variance (CV) has upper limit
$\sqrt{2/3}$. For two-coupled cells, we derive the partial differential
equations (PDEs) for the expected synchronized beating intervals and the
distribution density of phase. Moreover, we also consider the conventional
Kuramoto model for both two- and $N$-cells models, where we establish a new
analysis using stochastic calculus to obtain the CV of the ''synchronized''
beating interval, and make some improvement to the literature work.
