Desynchronization Control And Parameter Identification Of Neuronal Networks

Neurons in the brain connected with each other by synapse constitute the network, which isone of the most complex networks in this world. They, which reflect synapse flow in asynchronal way, process information in order to complete some complex brain functions such ascognitive function, motor function and memory function. Therefore, synchronization progressplays an important role in brain activities. However, the study shows that pathologically strongsynchronization process may badly injure the brain function, for example, resting tremor inParkinson’s disease and epilepsy. It is helpful to find a effective method to preventsynchronization for treat such disease. On the other band, because of its difficulty to performphysiological experiments, the study mode which takes the neural model as research objects hasbeen a major way to describe and understand the dynamics of the neuron system. And dynamicsof the neuron system are influenced by its parameters and topology. In this paper,desynchronization and topology identification of the neuron network will be studied.Two controllers are suggested for desynchronization. One is Washout filter aided feedbackcontrol. The Rulkov map model, which is a more computationally efficient neuronal model, ischosen to build globally coupled network, small-world network and scale-free network.Simulation results verify it is effective in numerical simulation and theory analysis, and theeffective range of parameters is given. The other one is the dynamical delayed feedbackcontroller. Rulkov map model and Hindmarsh-Rose (HR) model are selected as nodes in theglobally coupled network, which can reproduce the synchronous behavior by adjusting values ofparameters. Simulation results demonstrate its effectivity. Moreover, it can be proved that twocontrollers are noninvasive, that is, the stimulus signals tend to zero once the network has beencontrolled.On the other hand, adaptive methods based on lag synchronization and anticipatorysynchronization respectively are proposed for topology identification of uncertain nonlinearlycoupled complex networks. The main idea is to build a response system, and then an adaptivecontroller is designed to realize the synchronization between the response and the drive system.In this process, the identification criteria of network topology and system parameters areobtained.A realistic neural model will be built via an exact parameter estimator, which is beneficial toreveal the working mechanism, firing pattern and dynamics of the neuron network. A logicaldesynchronization controller is helpful to neurological diseases induced by synchronization.