Modelling and Estimation of Chaotic Biological Neurons

In this paper an array of non-identical, locally connected chaotic biological neurons are modelled by a single representative chaotic neuron model based on an extension of the Hindmarsh-Rose neuron. This model is then employed in conjunction with the unscented Kalman filter to study the associated state estimation problem. The archetypal system, which was deliberately chosen to be chaotic, was corrupted with noise. The influence of noise seemed to kill the chaotic behaviour. Consequently it was observed that the filter performs quite well in reconstructing the states the system although the introduction of relatively low noise had a profound effect on the system. Neither the noise corrupted process model nor the filter gave any indications of chaos. We believe that this behaviour can be generalised and expect that unscented Kalman filtering of the states of a biological neuron to be completely feasible even when the uncorrupted process model exhibits chaos.