@article{10.1371/journal.pcbi.1002560, doi = {10.1371/journal.pcbi.1002560}, author = {Wilson, M. T. AND Robinson, P. A. AND O'Neill, B. AND Steyn-Ross, D. A.}, journal = {PLOS Computational Biology}, publisher = {Public Library of Science}, title = {Complementarity of Spike- and Rate-Based Dynamics of Neural Systems}, year = {2012}, month = {06}, volume = {8}, url = {https://doi.org/10.1371/journal.pcbi.1002560}, pages = {1-1}, abstract = {Relationships between spiking-neuron and rate-based approaches to the dynamics of neural assemblies are explored by analyzing a model system that can be treated by both methods, with the rate-based method further averaged over multiple neurons to give a neural-field approach. The system consists of a chain of neurons, each with simple spiking dynamics that has a known rate-based equivalent. The neurons are linked by propagating activity that is described in terms of a spatial interaction strength with temporal delays that reflect distances between neurons; feedback via a separate delay loop is also included because such loops also exist in real brains. These interactions are described using a spatiotemporal coupling function that can carry either spikes or rates to provide coupling between neurons. Numerical simulation of corresponding spike- and rate-based methods with these compatible couplings then allows direct comparison between the dynamics arising from these approaches. The rate-based dynamics can reproduce two different forms of oscillation that are present in the spike-based model: spiking rates of individual neurons and network-induced modulations of spiking rate that occur if network interactions are sufficiently strong. Depending on conditions either mode of oscillation can dominate the spike-based dynamics and in some situations, particularly when the ratio of the frequencies of these two modes is integer or half-integer, the two can both be present and interact with each other.}, number = {6}, }