Effects of the parameters on the oscillation frequency of Izhikevich spiking neural networks

Abstract

Computational neuroscience attempts to understand the nervous system functions by using realistic models in large-scale simulations. This work is inspired by the Theory of Neural Group Selection (TNGS) and by the theory of Central Pattern Generators (CPGs). The TNGS states that neural connection topology generates strongly connected neuronal groups which are the smallest functional unit of the nervous system responsible for the most basic processing activities. The CPGs are neuronal circuits, located in the spinal cord of vertebrate animals, responsible for breathing, rhythm generation, motor behaviors, as well as other oscillatory functions. In this work, the oscillatory dynamics of neuronal groups and CPGs is modeled by using spiking neural networks. The aim is to analyze how the relationship between the parameters of the neural network influences its oscillatory frequency. The neurons are implemented by using the Izhikevich neuron model due to its low computational cost and biological plausibility. The methodology used in this analysis consists of four steps. In the first step, the influence of the constructive parameters in the oscillation frequency of the neural network is studied using the 2k Factorial Design. In the second step, the statistical relevance of the parameters a and b of the Izhikevich equation as well as the synaptic weight s was verified by the Friedman test, demonstrating their influence in determining the network oscillation frequency. In the third step, the parameters of the second step were adjusted to build systems at frequencies of 5, 20 and 40 Hz, proving the hypothesis established in the Friedman test, i.e., that the oscillation frequency can be set by the parameters a, b and s. In the fourth step, a mathematical formulation is presented to relate the oscillation frequency of the neural network with its constructive parameters. These results contribute to building spiking neural networks oscillating at desired frequencies, which may be used as the building blocks of CPGs and neuronal groups, as proposed in the TNGS.