Statistical pulse dynamics in a reaction-diffusion system

We study a nonlinear response to random external stimuli in an excitable reaction-diffusion system. Numerical simulations are carried out in one dimension to investigate formation of excited domains (pulses) in response to stimuli and pair-annihilate upon collision. Our main concern is how the area of excited domains in the steady state depends on the strength of stimuli. We have found three different stimuli-response behaviors: a power law dependence for sufficiently weak stimuli, a logarithmic dependence for intermediate strength and an oscillatory behavior for strong stimuli. The power law behavior can be understood by a theoretical analysis.