ArticleBiological cybernetics2022
Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition.
Article in Biological cybernetics, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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Who cites it
4 citing papers in PubMed.
- Emergence of multifrequency activity in a laminar neural mass model.PLoS computational biology · 2026Article
- Modelling dysfunction-specific interventions for seizure termination in epilepsy.NPJ systems biology and applications · 2025Article
- Firing rate distributions in plastic networks of spiking neurons.Network neuroscience (Cambridge, Mass.) · 2025Article
- Duality between predictability and reconstructability in complex systems.Nature communications · 2024Article
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3 authors.
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Abstract
Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system to describe the evolution of the average firing rates of the populations. In the present work, we investigate the impact of the often neglected refractory state and show that taking it into account can introduce new dynamics. Starting from a continuous-time Markov chain, we perform a rigorous derivation of a mean-field model that includes the refractory fractions of populations as dynamical variables. Then, we perform bifurcation analysis to explain the occurrence of periodic solutions in cases where the classical Wilson-Cowan does not predict oscillations. We also show that our mean-field model is able to predict chaotic behavior in the dynamics of networks with as little as two populations.
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