Stochastic generation and shifts of phantom attractors in the 2D Rulkov model

In this paper, a new stochastic phenomenon of the noise-induced shift of random states of the stochastically forced system into the domain of the phase plane where the original unforced deterministic system does not have any attractors is studied. Previously, this phenomenon called a "phantom" attractor was observed only for continuous-time dynamical models. The present paper shows that "phantom" attractors can be generated in the discrete-time models too. To analyze location of "phantom" attractors in the map-based Rulkov model, the method of "freezing and averaging" is used. The critical intensities of noise that causes the onset of "phantom" attractors are estimated by the confidence domains method based on the stochastic sensitivity function technique. (c) 2022 Published by Elsevier Ltd.