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This paper investigates the effect of double-frequency excitation on a fractional cerebral aneurysm model at the circle of Willis, where two kinds of external excitation are caused by the heart and arrhythmia respectively. Firstly, numerical analysis is performed on the proposed fractional model by using bifurcation diagrams and phase diagrams, and it is found that the periodic solution windows and chaotic solution windows switch more frequently than that resulted from single-frequency excitation, as a consequence of simultaneous resonances. Then, by using the method of multiple scales, the primary resonance response equation is obtained, and the effects of the system parameters on the amplitude of the fractional cerebral aneurysm model is analytically investigated. It is shown that double-frequency excitation changes the vibration patterns of the system under single-frequency excitation, and makes the primary resonance curve of the system deviate. Finally, the flexibility of using the amplitude-frequency equation to estimate the amplitude of the resonant solutions is verified numerically. [ABSTRACT FROM AUTHOR]

A fractional-order model is proposed to describe the dynamic behaviors of the velocity of blood flow in cerebral aneurysm at the circle of Willis. The fractional-order derivative is used to model the blood flow damping term that features the viscoelasticity of the blood flow behaving between viscosity and elasticity, unlike the existing fractional models that use fractional-order derivatives to replace the integer-order derivatives as mathematical/logical generalization. A numerical analysis of the nonlinear dynamic behaviors of the model is carried out, and the influence of the damping term and the external power supply on the nonlinear dynamics of the model is investigated. It shows that not only chaos via period-doubling bifurcation is observed, but also two additional small period-doubling-bifurcation-like diagrams isolated from the big one are observed, a phenomenon that needs further investigation. [ABSTRACT FROM AUTHOR]