Journal
APPLIED MATHEMATICAL MODELLING
Volume 101, Issue -, Pages 503-516Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2021.09.003
Keywords
MHR neuron model; Generalized Hamiltonian function; Firing pattern; Memristor; Electromagnetic induction; Band-limited white noise
Funding
- National Natural Science Foundation of China [61873186]
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This paper introduces a novel 4D HR model with a threshold flux-controlled memristor, which describes the electromagnetic induction effect. Compared to existing models, this model can more simply describe the dynamics of neuronal electrical activities and uncovers hidden dynamics.
It has been extensively studied to employ memristors to model the relationship between the electromagnetic field and the membrane potential, especially for the research of mod-eling and dynamical analyses of electrical activity using HR neurons with memristors. This paper proposes a novel 4D HR model with a threshold flux-controlled memristor (MHR), which describes the electromagnetic induction effect. The proposed 4D HR model retains the original HR properties and can describe the complex dynamics of neurons' electrical activities with fewer parameters than the existing models. Due to the particularity of the no equilibrium point of the MHR model, the hidden dynamics are found in the proposed MHR model. The generalized Hamiltonian function is fully derived for the MHR neuron model using Helmholtz's theorem. The simplest form of the Hamiltonian form is given by assigning special values. The average Hamiltonian energy and its bifurcation are employed to find the connection between energy and firing patterns. The band-limited white noise is also studied, and it is found that it positively influences the electrical activities in the proposed MHR system. (c) 2021 Elsevier Inc. All rights reserved.
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