Analysis of a chaotic spiking neural model: The NDS neuron

TL;DR

This paper analyzes and enhances the chaotic NDS neuron model, exploring its dynamics, stability, and potential for memory representation, emphasizing chaos's role in neural computation.

Contribution

It introduces methods to improve the NDS model by parameter scaling and discretization analysis, revealing insights into its attractor dynamics and stability.

Findings

Parameter scaling affects NDS dynamics and stability.

Discretization methods influence the model's chaotic behavior.

NDS can stabilize to multiple unstable periodic orbits, suggesting memory capacity.

Abstract

Further analysis and experimentation is carried out in this paper for a chaotic dynamic model, viz. the Nonlinear Dynamic State neuron (NDS). The analysis and experimentations are performed to further understand the underlying dynamics of the model and enhance it as well. Chaos provides many interesting properties that can be exploited to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization.Chaos might play an important role in information processing tasks in human brain as suggested by biologists. If artificial neural networks (ANNs) is equipped with chaos then it will enrich the dynamic behaviours of such networks. The NDS model has some limitations and can be overcome in different ways. In this paper different approaches are followed to push the boundaries of the NDS model in order to enhance it. One way is to study the effects of scaling the parameters of the chaotic equations of the NDS model and study the resulted dynamics. Another way is to study the method that is used in discretization of the original R\"{o}ssler that the NDS model is based on. These approaches have revealed some facts about the NDS attractor and suggest why such a model can be stabilized to large number of unstable periodic orbits (UPOs) which might correspond to memories in phase space.