  The microquasar GRS 1915+105 is known to exhibit a very variable X-ray
emission on different time scales and patterns. We propose a system of two
ordinary differential equations, adapted from the Hindmarsh-Rose model, with
two dynamical variables x(t), y(t) and an input constant parameter J_0, to
which we added a random white noise, whose solutions for the x(t) variable
reproduce consistently the X-ray light curves of several variability classes as
well as the development of low frequency Quasi-Periodic Oscillations (QPO). We
show that changing only the value of J_0 the system moves from stable to
unstable solutions and the resulting light curves reproduce those of the
quiescent classes like phi and chi, the delta class and the spiking rho class.
Moreover, we found that increasing the values of J_0 the system induces high
frequency oscillations that evolve to QPO when it moves into another stable
region. This system of differential equations gives then a unified view of the
variability of GRS 1915+105 in term of transitions between stable and unstable
states driven by a single input function J_0. We also present the results of a
stability analysis of the equilibrium points and some considerations on the
existence of periodic solutions.
