A bidirectional associative memory model with almost periodic endogenous and exogenous stimuli

Díaz-Marín, Homero G.; Osuna, Osvaldo; Villavicencio-Pulido, Jose; Geiser

doi:10.22124/jmm.2024.27489.2420

A bidirectional associative memory model with almost periodic endogenous and exogenous stimuli

Document Type : Research Article

Authors

¹ Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana. Edif. Alfa, Ciudad Universitaria, C.P. 58040. Morelia, Michoacán, México

² Instituto de Física y Matemáticas, Universidad Michoacana. Ciudad Universitaria, C.P. 58040. Morelia, Michoacán, México

³ División de Ciencias Biológicas y de la Salud, Depto. de Ciencias Ambientales, Universidad Autónoma Metropolitana Unidad Lerma, Av. Hidalgo Poniente No. 46, Col. La Estación, 52006 Lerma de Villada, Edo. de México, México

10.22124/jmm.2024.27489.2420

Abstract

In this work, a two-neuron model that describes a module of a neuronal network is analyzed. Unlike other studies, all the rates involved in the model are asumed to be almost periodic functions. Assuming an almost periodicity in the neuronal mechanisms offers advantages because the endogenous and exogenous stimuli received by the neuron are not necesarilly periodic or constant. Analysis of the model showed that it is associated with a unique stable almost periodic solution when some conditions on the parameters of the model are satisfied. Numerical simulations of the solutions of the model show that the neuronal state variable of both neurons can be underestimated or overestimated depending on whether the neuronal dynamics is modeled by periodic or almost periodic functions. Such estimation errors can lead to failure in forecasting the time in which neurons must synchronize.

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