Abstract
A quantitative mathematical model of neurons should not only include enough details to consider the dynamics of single neurons but also minimize the complexity of the model so that the model calculation is convenient. The two-dimensional Prescott model provides a good compromise between the authenticity and computational efficiency of a neuron. The dynamic characteristics of the Prescott model under external electrical stimulation are studied by combining analytical and numerical methods in this paper. Through the analysis of the equilibrium point distribution, the influence of model parameters and external stimulus on the dynamic characteristics is described. The occurrence conditions and the type of Hopf bifurcation in the Prescott model are analyzed, and the analytical determination formula of the Hopf bifurcation type in the neuron model is obtained. Washout filter control is used to change the Hopf bifurcation type, so that the subcritical Hopf bifurcation transforms to supercritical Hopf bifurcation, so as to realize the change of the dynamic characteristics of the model.
Highlights
Computational neuroscience emphasizes quantitative research methods and studies the nervous system at different levels through mathematical analysis and computer simulation [1]
Neuron is the smallest unit of the nervous system, and its structure and properties determine the functional characteristics of the neuron network [2]. erefore, only by understanding the characteristics and activity of single neurons can we further understand the mystery of neuron networks and even the operation of the brain
It is necessary to include enough details to consider the dynamics of a single neuron and to minimize the complexity of the model and retain its essential characteristics so that the model calculation is convenient [3]. e two need to reach a balance
Summary
Computational neuroscience emphasizes quantitative research methods and studies the nervous system at different levels through mathematical analysis and computer simulation [1]. Supercritical Hopf bifurcation is a stable equilibrium point that loses stability and produces a limit cycle attractor with a small amplitude. Zhou et al studied the local dynamic behaviors including stability and Hopf bifurcation of a four-dimensional hyperchaotic system with both analytical and numerical methods [17]. Bao et al investigated the stability transitions of the stable and unstable equilibrium states via fold and Hopf bifurcations in a two-dimensional nonautonomous tabu learning neuron model [18]. Few researchers have studied controlling of the bifurcation type of the twodimensional Prescott model by means of Washout filter. This paper uses the theoretical method of nonlinear dynamics to study the bifurcation characteristics of the Prescott model. The bifurcation characteristics of the model are controlled using Washout filter
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