The Chaos And The Complexity of the Abnormal Oscillations Propagation in A 2-D Strong Coupling Neuronal Network

The abnormal oscillations propagation in an actual neural tissue is often irregular and complex so that it can't be understood thoroughly until now, however some special work can prove helpful. In our work, a 2-D network is built where the nonlinear oscillators are coupled via resistors. Based on the network, a 2-D spatial-temporal partial differential equation (PDE) is presented to investigate the turbulence caused by the abnormal oscillations propagation. In the PDE, the Chay model is regarded as an oscillator that gives some abnormal oscillations. Resistors represent the effect of gap junctions. The Lyapunov exponent and the approximate entropy (ApEn) are applied to the analysis for the chaos and the complexity in the propagation. Numerical results show that the nonlinear and the complexity of the activity are large when the activity is affected by the abnormal propagation. It is also indicated that neurons in distinct state behave differently when affected by the propagation. Although, the theoretical work is so limited far to explain all problems in disorder, the theoretical work can be helpful to understand the new oscillations giving birth to during the abnormal oscillations propagation