Adaptive exponential integrate-and-fire model with fractal extension

Autor(es)

Souza, Diogo L. M. ; Gabrick, Enrique C. ; Protachevicz, Paulo R. ; Borges, Fernando S. ; Trobia, Jose ; Iarosz, Kelly C. ; Batista, Antonio M. ; Caldas, Ibere L. ; Lenzi, Ervin K.

• Tipo de documento: Artigo Científico
• Fonte: Chaos; v. 34, n. 2, p. 9-pg., 2024-02-01.

Resumo

The description of neuronal activity has been of great importance in neuroscience. In this field, mathematical models are useful to describe the electrophysical behavior of neurons. One successful model used for this purpose is the Adaptive Exponential Integrate-and-Fire (Adex), which is composed of two ordinary differential equations. Usually, this model is considered in the standard formulation, i.e., with integer order derivatives. In this work, we propose and study the fractal extension of Adex model, which in simple terms corresponds to replacing the integer derivative by non-integer. As non-integer operators, we choose the fractal derivatives. We explore the effects of equal and different orders of fractal derivatives in the firing patterns and mean frequency of the neuron described by the Adex model. Previous results suggest that fractal derivatives can provide a more realistic representation due to the fact that the standard operators are generalized. Our findings show that the fractal order influences the inter-spike intervals and changes the mean firing frequency. In addition, the firing patterns depend not only on the neuronal parameters but also on the order of respective fractal operators. As our main conclusion, the fractal order below the unit value increases the influence of the adaptation mechanism in the spike firing patterns. (AU)

• Processo FAPESP: 18/03211-6 - Dinâmica não linear
• Beneficiário: Iberê Luiz Caldas
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 23/12863-5 - Sincronização em redes neuronais com plasticidade sináptica de longa duração
• Beneficiário: Paulo Ricardo Protachevicz
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 20/04624-2 - Plasticidade sináptica em redes neuronais
• Beneficiário: Paulo Ricardo Protachevicz
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado