Resonances of a fractional-order biomedical model with time delay state feedback

Abstract

In the present paper, the primary resonance of a fractional-order Willis aneurysm system with time-delay state feedback control is studied. Using the multiple scale method, the amplitude and phase equations are obtained. The first order approximate solution is derived and the influence of time delay on resonance is studied. The concept of equivalent damping related to time-delay feedback is proposed, and the reasonable selection of feedback gain and time delay is discussed from the point of view of vibration control. The frequency response and external excitation response curves of the system are given. In order to test the stability of the system, bifurcation analysis is carried out. The obtained results are very useful in the clinical diagnosis and treatment of cerebral aneurysms.