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Analysis of a chaotic spiking neural model: The NDS neuron
Aug 16, 2014
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.
Studying a Chaotic Spiking Neural Model
Oct 26, 2013
Dynamics of a chaotic spiking neuron model are being studied mathematically and experimentally. The Nonlinear Dynamic State neuron (NDS) is analysed to further understand the model and improve it. Chaos has many interesting properties such as sensitivity to initial conditions, space filling, control and synchronization. As suggested by biologists, these properties may be exploited and play vital role in carrying out computational tasks in human brain. The NDS model has some limitations; in thus paper the model is investigated to overcome some of these limitations in order to enhance the model. Therefore, the models parameters are tuned and the resulted dynamics are studied. Also, the discretization method of the model is considered. Moreover, a mathematical analysis is carried out to reveal the underlying dynamics of the model after tuning of its parameters. The results of the aforementioned methods revealed some facts regarding the NDS attractor and suggest the stabilization of a large number of unstable periodic orbits (UPOs) which might correspond to memories in phase space.
* Journal, 13 pages