The Chaotic Analysis Of The Circle Of The Cerebral Aneurysm Model With Pharmaceuticals

Cerebral aneurysm is a common malignant disease of residents in our country. The present studies on cerebral aneurysm were mainly in the field of integer order. In this paper, a novel fractional-order chaotic system is constructed and its fractional order is analyzed. Besides, this paper mainly studied the circle of the cerebral aneurysm model with pharmaceuticals. The effective control of antihypertensive drugs for cerebral aneurysm is investigated by the analysis of the phase portraits and Poincaré map.Firstly, fractional differential operator is applied to the Willis ring cerebral aneurysm system with damping term proposed by Cao Jinde et al. The equilibrium point of the new system was calculated and the stability of the equilibrium point was analysed based on the Lyapunov stability theory and fractional-order stability theory. The influence of fractional order to the new chaotic system is verified by the analysis of the state diagram and geometric graph.Secondly, a new model of the circle of Willis chaotic system was constructed through the introduction of antihypertensive drugs' inspirit function. Chaotic complex dynamic characteristics of the new model were analyzed, including the existence of chaotic attractor, the Lyapunov exponents and the Poincaré map. In addition, this paper discussed the influence of parameters on the chaotic model by numerical simulation.In the end, this paper discussed the effective control of antihypertensive drugs' inspirit function over blood flow velocity and blood flow acceleration by the phase portraits and Poincaré map. Numerical simulation indicated that antihypertensive drugs had an effect on cerebral aneurysm system.