5. Summary We have used an established neural field model of the corticothalamic system (Breakspear et al., 2006; Zhao and Robinson, 2015) along with a temporally varying connection strength between the cortex and the thalamus in order to study the dependence of model absence seizures on a physiological connection strength and its time course. Specifically, we investigated spectral and temporal characteristics of seizures by varying the maximum height, duration, and ramp rate of the coupling strength. Using these outcomes, it is also possible to qualitatively predict the effects of varying other connection strengths because they will exhibit similar dynamics due to the universality properties of the Hopf bifurcation. The key outcomes are:
(i) The system exhibits a ∼ 3 Hz limit cycle oscillation once the connection strength crosses the bifurcation threshold, which is the characteristic frequency of absence seizures. This is consistent with previous studies that showed that increasing the corticothalamic connection strength beyond a threshold can push the system into the seizure state via a supercritical Hopf bifurcation (Breakspear et al., 2006; Marten et al., 2009; Robinson et al., 2002; Zhao and Robinson, 2015). The system can be returned to the resting equilibrium by decreasing the connection strength below the threshold. However, in cases with νmax 6.2 mV s, the corticothalamic system may settle in a steady state close to Qmax .
(ii) The maximum amplitude φe reaches during oscillatory dynamics mostly depends on the maximum connection strength, νmax . Increasing νmax also increases the firing rate because an increase of the connectivity strength increases the strength of the negative feedback loop between the cortex and the thalamus and the amplitude of limit cycle.
