Model for a neural network structure and signal transmission

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Abstract
We present a model of a neural network that is based on the diffusion-limited-aggregation (DLA) structure from fractal physics. A single neuron is one DLA cluster, while a large number of clusters, in an interconnected fashion, make up the neural network. Using simulation techniques, a signal is randomly generated and traced through its transmission inside the neuron and from neuron to neuron through the synapses. The activity of the entire neural network is monitored as a function of time. The characteristics included in the model contain, among others, the threshold for firing, the excitatory or inhibitory character of the synapse, the synaptic delay, and the refractory period. The system activity results in “noisy” time series that exhibit an oscillatory character. Standard power spectra are evaluated and fractal analyses performed, showing that the system is not chaotic, but the varying parameters can be associated with specific values of fractal dimensions. It is found that the network activity is not linear with the system parameters, e.g., with the numbers of active synapses. The details of this behavior may have interesting repercussions from the neurological point of view.