Anomalous stochastic dynamics induced by the slip–stick friction and leading to phantom attractors

Abstract

Abstract A new phenomenon of phantom attractors appearing as a result of slip–stick friction force under the influence of stochastic forcing is revealed on the basis of simple nonlinear dynamical model. The abrupt stepwise transitions between the stable equilibria or cycles and floating phantom attractors are found at different “noise” - “no noise” shifts. Some unusual features of stochastic dynamics are connected with the fact that the system with small noise exhibits large amplitude oscillations while the noise of greater intensities induces the lesser stochastic fluctuations near the phantom attractor. The theory based on the separation of slow and fast dynamical variables is developed to predict the arrangement of phantom attractors.