Single neuron chaos

Single neuron dynamics can be mathematically modeled to include chaotic dynamics. On the basis of the model of W.S. McCullouch and W. Pitts (1943), it is shown that the output-input slope is closely related to the standard quadratic map of Feigenbaum. A nonlinear mapping of the threshold function consisting of two degrees of dynamic freedom is adopted to accommodate the refractory and replenishment periods of an axon hillock. By including a third degree of freedom that obeys the quadratic map of Feigenbaum and functions as an internal source term, the final neuron output can produce pulses with a deterministic chaos that depends on the input level