Abstract
In this work, we establish the existence of traveling fronts in a fractional-order formulation of the Amari neural field model. Fractional-order models act as a memory index of the underlying dynamical system. Therefore, in a fractional-order neural field model, we potentially incorporate the effect of neuronal collective memory. Considering Caputo's fractional derivative framework and a fractional-order of 0≤α≤1, we establish explicit front solutions that allow us to analyze frontspeed and frontshape features directly. Furthermore, considering an exponential synaptic connectivity kernel, we find a bifurcation on the effect of fractional-order on front features. In particular, we find the existence of a critical synaptic threshold, k⋆, that qualitatively modifies the effect of fractional order on frontspeed. Below this critical threshold, fractional-order increases frontspeed whereas, above this threshold, fractional-order decreases frontspeed. In particular, less fractional-order implies a more substantial impact on frontspeed (either by increasing or decreasing frontspeed). Also, we find that lower fractional orders imply, in general, a slower power-law tendency towards the excited state. Therefore, our results establish the presence of different dynamics in the propagation of spatio-temporal patterns on neural fields due to the incorporation of a fractional-order framework and a potential memory index.
Translated title of the contribution | Sobre la existencia de frentes viajeros en el modelo de campo neural de Amari de orden fraccional |
---|---|
Original language | English |
Article number | 106790 |
Journal | Communications in Nonlinear Science and Numerical Simulation |
Volume | 116 |
DOIs | |
State | Published - Jan 2023 |
Keywords
- Amari model
- Caputo derivative
- Fractional-order derivative
- Neural fields
- Traveling fronts