Controllability Anyalysis Of The Neural Dynamic Model

The neural dynamic model is a typical neural computation model of modeling real electroencephalography signal.The research on the controllability of the neural dynamic model can confirm the feasibility of the closed-loop modulation scheme based on the electroencephalography signal in theory,and provide a theoretical basis for the design of the control algorithm.The research on the controllability of the neural dynamic model also can further explore more effective modulation scheme,which provides theoretical references for the treatment of neurological and psychotic disorders by using the control theory.In this paper,the controllability of the neural dynamic model is analyzed quantitatively.The influences of dynamical parameters and network topology on the controllability in the neural dynamic model are analyzed by using system controllability theory and complex network theory.We do the following work:First,for the single neural dynamic model,the nonlinear system controllabiltiy matrix is built by Lie brackets concept,and the controllability index is built by the matrix condition number.The associations between the dynamic parameters and the controllability index are analyzed quantitatively,and then the influences of the dynamic parameters on the controllability of the single neural dynamic model are researched.Second,the multiple neural dynamic coupled model is built by using complex network theory.The local linearization method is used to linearize the multiple neural dynamic coupled model due to the highly nonlinear characteristics of the coupled model.Then the controllability index of the coupled model is built by the linear system controllability theory and the matrix condition number.The qualitative associations between dynamic parameters and controllability are further researched under the specific coupled parameters.Third,for the multiple neural dynamic coupled model that is dealt with the local linearization method,the controllability index is built by the linear system controllability matrix and matrix condition number.The associations between the network topology parameters and the controllability index of the coupled model are analyzed quantitativelybased on the controllability index,and then the influences of the network topology parameters on the controllability of the multiple neural dynamic coupled model are researched.