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.