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Numerical simulations are conducted to demonstrate our theoretical results and show the complexity of the model dynamics in Section 3, too.
The model dynamics in the macro- and the micro-region are both discussed and the controller design is separated into two parts to satisfy the requirements in each region.
Indeed, in light of this set of results, it is interesting that we do not always find this behavior for the LIF model with discrete input kicks, in the case where E + I − 2 E I < 0. This disparity in results for the LIF model points out that details of how synaptic inputs are modeled can influence model dynamics in significant ways.
The figure is referenced in the Results section "Model dynamics in response to natural sentences".
More details about the model are included in Appendix A. In the main analysis we focussed on a specific model parameterization and explored model dynamics in more detail in additional analyses that are provided in Appendix B. In the main analysis the number of groups was set to 1000 with 10 individuals per group, 10 conflict rounds and an initial fitness of individuals of 100.
Despite the fact that we use advanced adaptive-step integrators, for some parameter sets the ODE integration can fail, due to the discontinuities in the model dynamics: in that case or in the case of violation of the basic constraint about non-negative values for the simulated protein concentration, we simply discard the respective solution (by giving the objective function a very high real value).
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We note that the way in which these model dynamics vary in relation to coupling strength is very similar to the full neural mass model (see [13]).
This is signaling that the influence of gKCa and gA on the model dynamics is comparable in importance to the influence of other parameters.
The model dynamics are schematically represented in Figure 1 and the model parameters defined in Table 1.
A close up of these model dynamics can be seen in Fig. 3.
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