Consistency between modulational instability and energy localization in time-delay-memristive neural network

Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaoundé I P.O. Box 812, Yaoundé, Cameroon

^(a) E-mail: etemearmand@yahoo.fr (corresponding author)

Received: 9 June 2023
Accepted: 8 August 2023

Abstract

In this letter, we exclusively study the consistency between modulational instability and energy localization in a Hindmarsh-Rose–type memristive neural network under time-delay effect. Analytically, we find the suitable values of time-delay and memristor strength that support and control modulational instability. Also the Hamiltonian energy of the system is computed using the Helmholtz theorem. Numerical simulations are done to verify the analytical predictions. As a result, emission of action potential arises only in the domain where energy is highly localized, thus attesting that analytical predictions are in perfect agreement with numerical findings. These findings give more insight on relationship between modulational instability and energy localization in an excitable media along with the underlying biological phenomena that are involved.