Regular and stochastic auto-oscillations in the reological model

This paper is devoted to research of mathematical model of a suspension flow. For these flows, the transitions from stationary to the oscillatory regimes have been observed in experiments. Bifurcation analysis allows us to divide the space of parameters onto steady equilibria and limit cycles zones. Details of Hopf bifurcation depending on degree of system stiffness are investigated. On the basis of the stochastic sensitivity function technique, the parametrical analysis of influence of random disturbances on the system attractors is carried out. It is shown that as a system stiffness increases, the stochastic sensitivity of oscillations rises sharply. The narrow zone of super-sensitivity of oscillations was found. In this zone, even small background disturbances result in the essential fluctuations of their amplitude.