Control And Synchronization To The Chaos System Of Aneurysm Of Circle Of Willis

The systems of aneurysm of circle of Willis are nonlinear systems, which were built up only several years ago and have been developing day after day. They are based on clinical observations and outer-body simulation experiments, and related closely to biomedical meanings. The blood flow speed in aneurysms are taken as the main research object and the development of aneurysms are embodied by the hemodynamics of intracranial aneurysms at the site of circle of Willis .First we discuss fuzzy sliding control to the chaos system of aneurysm of circle of Willis.Combining fuzzy control with sliding control, we design controller for the change of blood stream in aneurysm. The controller has strong robust and can remove vibration in controlling.The method make the system track the given state variable and finally make the error approach to zero.Then we analyze the nonlinear feedback control to the circle of Willis chaos system. For each certain parameter, we propose the nonlinear feedback controller and prove the controller can make the system approach to a desired signal at an exponent rate. Based on this result ,the synchronization of Willis system with itself is analyzed. The method remove chaos of the system in theory and provide a proof for avoiding the aneurysm break. Finally we discuss the adaptive synchronization problem of two Willis chaotic system. Based on Lyapunov stability theory, we propose adaptiva controller making two systems with different parameters synchronize. The parameter of controller and estimate can provide scientific basis to use leechdom of the aneurysm. In theory, it has an effect on expanding blood stream and avoid spasticity. The method has the clinic sense to cure the aneurysm and provide a new problem in medicine. Its biomedicine is profound.