1. A method, comprising: maintaining neuron attributes for multiple neurons; maintaining a collection of axon activity bit maps for multiple axons, wherein each axon activity bit map corresponds to a particular time step, and the axon activity bit map maintains bits identifying incoming firing events for delivery to the multiple axons in the particular time step; and for each time step: integrating incoming firing events identified in an axon activity bit map corresponding to the time step in a time-division multiplexing manner, wherein the incoming firing events are integrated based on the neuron attributes; based on the integrated incoming firing events, generating an update vector identifying outgoing firing events generated by the multiple neurons, wherein at least one of the outgoing firing events targets an axon of the multiple axons in a different time step, and an axon activity bit map corresponding to the different time step is updated to include information identifying the at least one outgoing firing event for delivery to the axon in the different time step; and updating the neuron attributes based on the integrated incoming firing events.