A theoretical study for the chaos and complexity of the synchronous oscillations in electrically coupled abnormal neurons

Many experiments demonstrate that the synchrony of neurons is a hallmark in epileptic seizure and the dynamical process of the epilepsy is complex with new oscillations born. In fact, epileptic seizure is very complicated relating to many factors so that it can't be understood thoroughly only in some special aspect. Based on the previous work on synchronous oscillations of electrically coupled abnormal neurons, a theoretical effort is carried out to further investigate the chaos by Lyapunov exponent and phase portrait and degree of complexity by approximate entropy in the dynamical activities. It is concluded that the synchronous activities are chaotic and complex with new oscillations born and the values of Lyapunov exponent and approximate entropy are different with the electrical coupling strength. It is also found that the trend of approximate entropy is same as that of Lyapunov exponent in the study at the dynamical activity of the two electrical coupling neurons. In the synchrony of 2-D neuronal network, the values of Lyapunov exponent are almost much greater than that of the two electrical coupling neurons. The values of approximate entropy of the different neurons in the 2-D network have almost the same trend but approximate entropy of neuron in synchrony is greater than that of neuron in non-synchrony. It is indicated that the neurons in synchrony have greater ability to produce new oscillations than that in non-synchrony. The theoretical work is helpful to understand the pathological mechanism of new oscillations born in epilepsy from a nonlinear point of view.