Networks of Motoneurons with Mixed-Mode Oscillations

In this paper we study the role of Mixed-Mode Oscillations (MMOs), observed experimentally in motoneurons, in the dynamics of different networks. As control parameters we have the applied current (Iapp) and the coupling strength (Ggap) between pairs of neurons. By fixing the value of one of these parameters, we analyze the dynamics in the network with identical neurons via a synchrony measure (χ2) which gives the average fluctuations in the voltage with respect to the fluctuations in the voltage of single cells. To do so, we first compare the synchrony measure with the number of cells given a global coupling. Secondly, we compare χ2 with the number of connections among cells by changing the number of kth nearest neighbors. Finally, we look at small-world topologies to observe the dependance of χ2 on the randomness in the network. We also analyze the dynamics of a network with neurons in different regimes, these examples show the importance of mixed-mode oscillations in the overall behavior.