Effect of Dynamic Threshold on the Response and Bifurcation in a Space Clamped FHN Model with External Stimulus

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[Abstract] The neuronal models are known to exhibit a variety of firing patterns which mimic the spiking patterns of real neurons. Although the exhibited firing patterns are highly dependent on the type of neuron; a majority of these firing patterns could be mimicked by modulating various parameters of the simulated models. In the present work, the effect of the temporal variation of the threshold on the firing patterns of the FHN neuron model has been studied. By considering various deterministic (periodic, damped periodic and mixed mode) functions for the threshold we show that the firing patterns of the FHN model are in phase with the threshold function under consideration. But, up on addition of deterministic noise to the periodic threshold function, the firing patterns became incoherent. Further, the combined effect of external stimulus and mixed mode threshold variation on the FHN model has beenstudied. This was accomplished by constructing bifurcation diagrams of the corresponding map-based model. The continuous FHN model has been transformed into discrete system by applying forward Euler scheme which was further used for constructing the bifurcation patterns. The patterns in the obtained bifurcation diagrams indicate that the complexity underlying the dynamics of the aforementioned FHN system is sensitive to the nature of the external stimulus.

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