PREDICTING PERIOD-DOUBLING BIFURCATIONS AND MULTIPLE OSCILLATIONS IN NONLINEAR TIME-DELAYED FEEDBACK-SYSTEMS

In this brief, a graphical approach is developed from an engineering f requency-domain approach enabling prediction of period-doubling bifurc ations (PDB's) starting from a small, neighborhood of Hopf bifurcation points useful for analysis of multiple oscillations of periodic solut ions for time-delayed feedback systems. The proposed algorithm employs higher order harmonic-balance approximations (HBA's) for the predicte d periodic solutions of the time-delayed systems. As compared to the s ame study of feedback systems without time delays, the HBA's used in t he new algorithm include only some simple modifications. Two examples are used to verify the graphical algorithm for prediction: one is the well-known time-delayed Chua's circuit (TDCC) and the other is a time- delayed neural-network model.