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Bifurcation diagram of the one-neuron recurrent network. Horizontal axis is b, and vertical axis is x. The black curve is the set of stable and unstable equilibria. Notice that the system exhibits hysteresis, and can be used as a one-bit memory.

Bifurcation memory is a generalized name for some specific features of the behaviour of the dynamical system near the bifurcation. An example is the recurrent neuron memory.