The spiking of a neuron can be modeled by the differential
Chapter , Problem 19(choose chapter or problem)
The spiking of a neuron can be modeled by the differential equation d dt = 1 cos + (1 + cos )I(t), where I(t) is the input. Often the input function I(t) is a constant I. When is an odd multiple of , the neuron spikes. (a) Using HPGSolver, sketch three slope fields, one for each of the following values of I: I1 = 0.1, I2 = 0.0, and I3 = 0.1. (b) Calculate the equilbrium solutions for each of these three values. (c) Using the slope field, describe the long-term behavior of the solutions in each of the three cases.
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