Nonlinear Analysis And Control To A Class Of The Biomathematical Model

The biomathematical models of muscular blood vessel are nonlinear systems, which were built up only several years ago and have been developing day after day. They are related closely to biomedical meanings. We discuss the periodicity, the stability and chaos phenomena of the biomathematical models for two types of muscular blood vessel. The approximation solution of the biomathematical model of muscular blood vessel under the condition of the nonresonant case is obtained. The expansion method for two variables of perturbation theory is used and the approximation solutions are given to the biomathematical model of muscular blood vessel under two cases.Considering the biomathematical model of muscular blood vessel including disturbing term, we apply adaptive control method based on Backstepping and nonlinear feedback synchronization control to study the control and chaos synchronization of the biomathematical model. The system will be made globally stable and two chaos systems will made to be chaos synchronized under the circumstance of single variable drive and less energy.The above research theoretically has provided the significative reference information for the medicine diagnosis and the treatment. Meanwhile, it can offer certain basis for changing the function of muscular blood. From theory we can see that the vessel in spasticity can be controlled to the stable state or synchronize with normal blood vessel, which provides theory on preventing and curing some disease like myocardial infarction. Simulation results indicate effectiveness of those methods.