Homoclinics in the Reconstruction of Dynamic Systems From Experimental Data

The role of homoclinic effects in solution of a reconstruction problem of system attractors and model equations from experimental observable in the presence of external noise is investigated numerically. It is shown that the possibility of reconstruction essentially depends on character of origin system homoclinic trajectories and noise intensity. If the homoclinic structure belongs to the attractor, then the reconstruction results in restoration origin system attractors. A small noise influence causes in this case a small perturbation of attractors probability measure and practically disappears due to filtering properties of the reconstruction algorithm. The homoclinic structure does not belong to the attractor, then in the absence of noise the probability measure concentrates at the attractor, the structure of which is not defined by the homoclinics. The noise perturbation induces new regimes. Then the attractor structure essentially depends on the homoclinics structure and noise level. In this case the model system attractor of which reproduces “invisible” homoclinic structure, is obtained as a result of reconstruction.