Noise influence on spike activation in a Hindmarsh–Rose small-world neural network

We studied the role of noise in neural networks, especially focusing on its relation to the propagation of spike activity in a small sized system. We set up a source of information using a single neuron that is constantly spiking. This element called initiator x o feeds spikes to the rest of the network that is initially quiescent and subsequently reacts with vigorous spiking after a transitional period of time. We found that noise quickly suppresses the initiator's influence and favors spontaneous spike activity and, using a decibel representation of noise intensity, we established a linear relationship between noise amplitude and the interval from the initiator's first spike and the rest of the network activation. We studied the same process with networks of different sizes (number of neurons) and found that the initiator x o has a measurable influence on small networks, but as the network grows in size, spontaneous spiking emerges disrupting its effects on networks of more than about N = 100 neurons. This suggests that the mechanism of internal noise generation allows information transmission within a small neural neighborhood, but decays for bigger network domains. We also analyzed the Fourier spectrum of the whole network membrane potential and verified that noise provokes the reduction of main θ and α peaks before transitioning into chaotic spiking. However, network size does not reproduce a similar phenomena; instead we recorded a reduction in peaks' amplitude, a better sharpness and definition of Fourier peaks, but not the evident degeneration to chaos observed with increasing external noise. This work aims to contribute to the understanding of the fundamental mechanisms of propagation of spontaneous spiking in neural networks and gives a quantitative assessment of how noise can be used to control and modulate this phenomenon in Hindmarsh−Rose (H−R) neural networks.