Unconventional criticality, scaling breakdown, and diverse universality classes in the Wilson-Cowan model of neural dynamics
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American Physical Society
Helena Christina Piuvezam, Bóris Marin, Mauro Copelli, and Miguel A. Muñoz. Unconventional criticality, scaling breakdown, and diverse universality classes in the Wilson-Cowan model of neural dynamics. Phys. Rev. E 108, 034110. [https://doi.org/10.1103/PhysRevE.108.034110]
SponsorshipConsejería de Conocimiento; Instituto Interuniversitario Carlos I de Física Teórica y Computacional at the University of Granada; Investigación Universidad, Junta de Andalucía; Spanish Ministry; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior 88887.581360/2020-00 CAPES; Conselho Nacional de Desenvolvimento Científico e Tecnológico 23038.003069/2022-87, 308703/2022-7, 425329/2018-6 CNPq; Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco APQ-0642-1.05/18 FACEPE; European Regional Development Fund P20-00173 ERDF; Agencia Estatal de Investigación MICIN/AEI/10.13039/501100011033, PID2020-113681GB-I00 AEI
The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural networks at a mean-field level, e.g., assuming large fully connected networks. Moreover, its stochastic counterpart allows one to study fluctuation-induced phenomena, such as avalanches. Here we revisit the stochastic Wilson-Cowan model paying special attention to the possible phase transitions between quiescent and active phases. We unveil eight possible types of such transitions, including continuous ones with scaling behavior belonging to known universality classes—such as directed percolation and tricritical directed percolation—as well as six distinct ones. In particular, we show that under some special circumstances, at a so-called “Hopf tricritical directed percolation” transition, rather unconventional behavior is observed, including the emergence of scaling breakdown. Other transitions are discontinuous and show different types of anomalies in scaling and/or exhibit mixed features of continuous and discontinuous transitions. These results broaden our knowledge of the possible types of critical behavior in networks of excitatory and inhibitory units and are, thus, of relevance to understanding avalanche dynamics in actual neuronal recordings. From a more general perspective, these results help extend the theory of nonequilibrium phase transitions into quiescent or absorbing states.