Networks of spiking neurons can have persistently firing stable bump attractors to represent continuous spaces (like temperature). This can be done with a topology with local excitatory synapses and local surround inhibitory synapses. Activating large ranges in the attractor can lead to multiple bumps, that show repeller and attractor dynamics; however, these bumps can be merged by overcoming the repeller dynamics. A simple associative memory can include these bump attractors, allowing the use of continuous variables in these memories, and these associations can be learned by Hebbian rules. These simulations are related to biological networks, showing that this is a step toward a more complete neural cognitive associative memory
