  The microquasar GRS 1915+105, exhibits a large variety of characteristic
states, according to its luminosity, spectral state, and variability. The most
interesting one is the so-called rho-state, whose light curve shows recurrent
bursts. This paper presents a model based on Fitzhugh-Nagumo equations
containing two variables: x, linked to the source photon luminosity L detected
by the MECS, and y related to the mean photon energy. We aim at providing a
simple mathematical framework composed by non-linear differential equations
useful to predict the observed light curve and the energy lags for the
rho-state and possibly other classes of the source. We studied the equilibrium
state and the stability conditions of this system that includes one external
parameter, J, that can be considered a function of the disk accretion rate. Our
work is based on observations performed with the MECS on board BeppoSAX when
the source was in rho and nu mode, respectively. The evolution of the mean
count rate and photon energy were derived from a study of the trajectories in
the count rate - photon energy plane. Assuming J constant, we found a solution
that reproduces the x profile of the rho class bursts and, unexpectedly, we
found that y exhibited a time modulation similar to that of the mean energy.
Moreover, assuming a slowly modulated J the solutions for x quite similar to
those observed in the nu class light curves is reproduced. According these
results, the outer mass accretion rate is probably responsible for the state
transitions, but within the rho-class it is constant. This finding makes
stronger the heuristic meaning of the non-linear model and suggests a simple
relation between the variable x and y. However, how a system of dynamical
equations can be derived from the complex mathematical apparatus of accretion
disks remains to be furtherly explored.
