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- Wilten Nicola, Sue Ann Campbell
- Front. Comput. Neurosci.
- 2013

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be… (More)

- Wilten Nicola, Sue Ann Campbell
- Journal of Computational Neuroscience
- 2013

Recently, a class of two-dimensional integrate and fire models has been used to faithfully model spiking neurons. This class includes the Izhikevich model, the adaptive exponential integrate and fire model, and the quartic integrate and fire model. The bifurcation types for the individual neurons have been thoroughly analyzed by Touboul (SIAM J Appl Math… (More)

- Muhammad Dur-e-Ahmad, Wilten Nicola, Sue Ann Campbell, Frances K. Skinner
- Journal of Computational Neuroscience
- 2011

The hippocampus is a brain structure critical for memory functioning. Its network dynamics include several patterns such as sharp waves that are generated in the CA3 region. To understand how population outputs are generated, models need to consider aspects of network size, cellular and synaptic characteristics and context, which are necessarily ‘balanced’… (More)

- Wilten Nicola, Cheng Ly, Sue Ann Campbell
- SIAM Journal of Applied Mathematics
- 2015

Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the mean-field systems have a degree of frequency error and the networks analyzed often do not include noise when there is… (More)

- Wilten Nicola, Sue Ann Campbell
- SIAM J. Applied Dynamical Systems
- 2016

Mean-field systems have been recently derived that adequately predict the behaviors of large networks of coupled integrate-and-fire neurons [14]. The mean-field system for a network of neurons with spike frequency adaptation is typically a pair of differential equations for the mean adaptation and mean synaptic gating variable of the network. These… (More)

- Katie A. Ferguson, Felix Njap, Wilten Nicola, Frances K. Skinner, Sue Ann Campbell
- Journal of Computational Neuroscience
- 2015

Determining the biological details and mechanisms that are essential for the generation of population rhythms in the mammalian brain is a challenging problem. This problem cannot be addressed either by experimental or computational studies in isolation. Here we show that computational models that are carefully linked with experiment provide insight into… (More)

Populations of neurons display an extraordinary diversity in the types of problems they solve and behaviors they display. Examples include generating the complicated motor outputs involved in grasping motions to storing and recalling a specific song for songbird mating. While it is still unknown how populations of neurons can learn to solve such a diverse… (More)

- Wilten Nicola, Felix Njap, Katie Ferguson, Frances Skinner, Sue Ann Campbell
- BMC Neuroscience
- 2014

Mean field analysis gives accurate predictions of the behaviour of large networks of sparsely coupled and heterogeneous neurons Large networks of integrate-and-fire (IF) model neurons are often used to simulate and study the behaviour of biologically realistic networks. However, to fully study the large network behaviour requires an exploration of large… (More)

- Wilten Nicola, Bryan P. Tripp, Matthew Scott
- Front. Comput. Neurosci.
- 2016

A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix… (More)

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be… (More)