Dynamical Characteristics Of The Epileptic Brain At Rest

ABSTACT:The basic structural unit of the nervous system is the neuron, and the burst-ing activity involves complex physical and chemical processes, and shows rich nonlin-ear dynamical behaviors. Nervous system consists of a large number of neurons, and all neurons are closely contacted by electrical synapses and chemical synapses. All neuron-s can be regarded as a high-dimensional, multi-level, multi-time scale, multi-functional complex information network structure, which is a complex network dynamical system. The synchronization is a hot topic of the nonlinear field, but some synchronizations of neurons often lead to certain neurological diseases, such as epilepsy and so on. This kind of synchronization is called the morbid synchronization. The study of pathological synchronization is necessary by using the basic theory of nonlinear dynamics.In this paper, at first based on EEG data corresponding to normal brains and epilep-tic brains from experiments and chaotic Rulkov neuron model, a simple system consist-ing of19neurons is established coupled by the electrical connection. The fixed points and the synchronization manifold of the system are given. We use the master stability function method to analyze the stability of the system, and the conditions of the stable fixed points and the emergences of bifurcations are given.Secondly, the dynamical characteristics associated with the normal brain and the epileptic brain at rest are taken into account. Judged by the eigenvalues of Jacobian ma-trix of the whole system, the synchronization manifold of the epileptic brain is unstable. From the raster plot and the waveform of the whole system, the epileptic brain arises abnormal synchronization, and the bursting time is relatively longer and more disorder.Finally, we summarize this paper. What we have done provides a basic mathemati-cal foundation for a more comprehensive research of the change of situation of patients with epilepsy at rest.