Effects of Time Delay on the Resonance Frequency of Andronov-Hopf Bifurcations in Neuromorphic Devices

Tunability is the property that the resonance frequency of an oscillator can be controlled to some degree. Subsequently, the tunability enhancements by introducing delayed feedback are discussed in detail. This is done by analyzing the bifurcation of the normal form of the super-critical Andronov-Hopf bifurcation with delayed feedback. For this analysis, it is assumed that the damping, the feedback, and the delay can be assigned arbitrarily. If the delay is assumed to be the bifurcation parameter, infinitely many Andronov-Hopf bifurcation emerge under certain conditions on the feedback and the damping. In addition to the bifurcations, the resonance frequency of this particular oscillator becomes tunable in terms of the damping and delayed feedback, such that the resonance frequency can be increased and decreased by assigning the parameters accordingly.