  Noise induced Brownian dynamics in underdamped medium is studied numerically
to understand the firing time of excitable systems. By considering Brownian
particles that move in underdamped medium, we study how the first arrival time
behaves for different parameters of the model. We study the first arrival time
for both single particle as well as the first arrival time of one particle out
a system that has N particles. The present study helps to understand the
intercellular calcium dynamics in cardiac tissue at the level of a single
microdomain and at a tissue level (ensemble of microdomains). In the presence
of time varying signal, we study how signal to noise ratio (SNR) depends on the
model parameters. It is showed that the SNR exhibits a pronounced peak at a
particular noise strength. The fact that the SNR is amplified as the number of
micro domains (N) increase shows that the weak periodic signal plays a decisive
role in controlling the noise induced dynamics of excitable systems which may
also shed light on how to control the abnormal calcium release in a cardiac
tissue.
