DYNAMICS OF A SINGLE MODEL NEURON

The parametrized dynamics of a standard nonlinear model neuron with self-interaction is discussed. For units with a self-excitatory connection a hysteresis effect is observed, and the underlying mechanism is identified as that of a cusp catastrophe. This is true for discrete as well as for continuous dynamics. For the discrete dynamics of self-inhibiting units there appear period-doubling bifurcations from stationary states to stable period-2 orbits.

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