Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data

NATALI GUISANDE; MONSERRAT PALLARES DI NUNZIO; NATANIEL MARTINEZ; OSVALDO A ROSSO; FERNANDO MONTANI

Conferencia; 3rd LATIN AMERICAN CONFERENCE ON COMPLEX NETWORKS, CUZCO, PERU, 21-25 August 2023; 2023

One of the most studied examples of nonlinear dynamical systems exhibiting chaotic behavior is the Hénon map. This discrete-time dynamical systemtakes a point (xn, yn) in the plane and maps it to a new point. Brain activities exhibit chaotic behaviors and their dynamics can be simulated by theoutputs of chaotic systems such as the Hénon map. However, these empirical observations lack theoretical support. Experiments in certain regionsof the cerebral cortex suggest that the spiking activity of neuronal populations is regulated by common non-Gaussian inputs across neurons. In thispaper we study the deviations from the random walk simulated by processes that exhibit distributions with deformations beyond a Gaussian statistic insingle-threshold neurons. And the scaling properties in large neuronal populations are investigated. The effect of synaptic interaction as well as structuralconnectivity on the synchronization transition in neural networks is considered. Synaptic plasticity at the level of pairs and triplets in the neuronalpopulation is taken into account by implementing a network of excitatory and inhibitory neurons that emulate the activity of the cerebral cortex. It isshown that the Hénon maps have equivalent dynamics to those of nonlinear models with non-Gaussian inputs and to models of neuronal populationswith synaptic plasticity that exhibit interactions through pairs and triplets of spikes.