A. A. Abramian
Institute for Problems of Mechanical Engineering,
Russian Academy of Sciencies,
V.O.Bolshoy pr.61, 199178 St.Petersburg, RUSSIA,
S. A. Vakulenko
Institute for Problems of Mechanical Engineering,
Russian Academy of Sciencies,
V.O.Bolshoy pr.61, 199178 St.Petersburg, RUSSIA,
We consider stability of special dynamical systems under a random noise. These systems (networks) are important in many applications. We focus our attention on supporting of homeostasis of these systems with respect to fluctuations of an external medium (the problem is posed by M. Gromov, A.Carbone ). Using a measure of stochastic stability we show that a network with fixed parameters is always unstable, i.e., the probability to support homeostasis converges to zero as time T tends to infinity.