Similar local neuronal dynamics may lead to different collective behavior

SÁNCHEZ DÍAZ, M; AGUILAR TREJO, E.; MARTIN, D.A.; CANNAS, S. A.; GRIGERA, T.S.; CHIALVO, DANTE R.

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2021 vol. 104 p. 64309 - 64309

1539-3755

This report is concerned with the relevance of the microscopic rules that implement individual neuronalactivation, in determining the collective dynamics, under variations of the network topology. To fix ideas westudy the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the buildingblocks of large-scale neuronal networks. One model, due to Greenberg and Hastings (GH), can be describedby evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi andCopelli (KC), represents an abstract branching process, where a single active neuron activates a given numberof postsynaptic neurons according to a prescribed ?activity? branching ratio. Despite the apparent similaritybetween the local neuronal dynamics of the two models, it is shown that they exhibit very different collectivedynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimesas the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuousdynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independentlyof the network topology. These results highlight the importance of paying attention to the microscopic ruleschosen to model the interneuronal interactions in large-scale numerical simulations, in particular when thenetwork topology is far from a mean-field description. One such case is the extensive work being done in thecontext of the Human Connectome, where a wide variety of types of models are being used to understandthe brain collective dynamics.