  Continuous "bump" attractors are an established model of cortical working
memory for continuous variables and can be implemented using various neuron and
network models. Here, we develop a generalizable approach for the approximation
of bump states of continuous attractor networks implemented in networks of both
rate-based and spiking neurons. The method relies on a low-dimensional
parametrization of the spatial shape of firing rates, allowing to apply
efficient numerical optimization methods. Using our theory, we can establish a
mapping between network structure and attractor properties that allows the
prediction of the effects of network parameters on the steady state firing rate
profile and the existence of bumps, and vice-versa, to fine-tune a network to
produce bumps of a given shape.
