Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback

Schneider, Felix M.
Schoell, Eckehard
Dahlem, Markus A.
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The onset of pulse propagation is studied in a reaction-diffusion (RD) model with control by augmented transmission capability that is provided either along nonlocal spatial coupling or by time-delayed feedback. We show that traveling pulses occur primarily as solutions to the RD equations while augmented transmission changes excitability. For certain ranges of the parameter settings, defined as weak susceptibility and moderate control, respectively, the hybrid model can be mapped to the original RD model. This results in an effective change of RD parameters controlled by augmented transmission. Outside moderate control parameter settings new patterns are obtained, for example step-wise propagation due to delay-induced oscillations. Augmented transmission constitutes a signaling system complementary to the classical RD mechanism of pattern formation. Our hybrid model combines the two major signaling systems in the brain, namely volume transmission and synaptic transmission. Our results provide insights into the spread and control of pathological pulses in the brain.
Nonlinear Sciences - Pattern Formation and Solitons