CHAOS AND COMPLEXITY IN ABNORMAL OSCILLATIONS OF TWO EXCITABLE NEURONS AND A 2D NETWORK MODEL COUPLED VIA GAP JUNCTIONS

Many electrophysiological experiments have shown that epileptic seizures often originate from the synchronous activities of abnormally excitable neurons. The dynamic process of epilepsy is very complex, and characterized by a seemingly rapid and dramatic birth of new oscillations, essentially leading to a propagation and amplification of the original aberrant activity. It is very difficult to thoroughly understand the mechanism from a theoretical standpoint, however some special work can prove helpful. Here we present a theoretical framework to investigate chaos and complexity in the synchrony of excitable neurons in an effort to study the collective oscillations within a neural network. As endogenous rhythms, oscillations arise because most cellular processes contain feedback. The Chay model of excitable neurons is chosen because the model describes the abnormal process, where spiking can be transformed into bursting via bifurcation. In our study, the Chay model is regarded as an abnormal oscillator and coupled via a resistor representing the effect of gap junctions (electrical synapses). In this paper, we present some models developed from the original Chay model, for the synchrony of two cells and a 2D neural network. Lyapunov exponent and phase portrait are utilized to evaluate the chaotic dynamics. Finally, approximate entropy is utilized to measure its complexity. Our results show that the synchrony of abnormal oscillations can occur when the coupling strength of the gap junction is sufficiently large. It is also found that the concentration of Ca 2+ ions does not synchronize. In the 2D network, approximate entropies of different oscillations with strong coupling strength are greater than those with weak coupling strength. It is indicated that synchronous neurons have greater ability to produce new oscillations than asynchronous ones. This work shows that nonlinear analytical methods may prove useful in elucidating the mechanisms of pathologic conditions, where new oscillations are born and propagated, such as in epilepsy.