分数阶Willis环脑动脉瘤的混沌动力学分析及控制

he Willis aneurysm systems (WAS) has some limitations in the description of the complex hemodynamic mechanism of the blood which often showed viscoelastic in the vascular system with complicated elasticity. For this reason, we propose fractional Willis aneurysm systems (FWAS) by applying the Caputo fractional differential and its theory in our article at first time. Firstly, the existence and uniqueness of solutions for FWAS are investigated theoretically. Then, we prove that the FWAS has chaotic characteristic by the analysis of the phase portraits and Poincare? section, and is a rational extension of its integer order form. Finally, we use two methods to control the chaotic FWAS respectively. One is that designing a suitable controller based on the stability theorem of fractional nonlinear non-autonomous system. The other is using pulse control by taking the drug's inspirit function as impulse function. Numerical simulations show the feasibility and effectiveness of the proposed two methods. The discussions about FWAS in our article have some theoretical significance for the research of cerebral aneurysm.