Abstract
A ghostbursting model is a mathematical model (a system of coupled nonlinear ordinary differential equations) that is based on the Hodgkin-Huxley formalism. The ghostbursting model describes bursting similar to the in vitro bursting of electrosensory neurons of weakly electric fish. Doiron and coworkers have focused on two system parameters of the model: maximal conductance of the dendritic potassium current and the current injected into the somatic compartment . They performed bifurcation analysis and revealed that the -parameter space was divided into three dynamical states: quiescence, periodic tonic spiking, and bursting. The present study focused on a third system parameter: the time constant of dendritic potassium current inactivation . A computer simulation of the model revealed how the dynamical states of the -parameter space changed in response to variations of .
Highlights
Hodgkin and Huxley [1] proposed a mathematical model that is composed of a system of four-coupled nonlinear ordinary differential equations and that describes the action potential regeneration of the squid giant axon and the biophysical mechanisms underlying the action potential generation
The present study shows that the regions of these dynamical states
In the present study, we performed a simulation of the model with gDr,d, Is variable values set at τ pd = 5.0 ms (Figure 2(b)), which was the same condition as that used in Figure 6 in [8]
Summary
Hodgkin and Huxley [1] proposed a mathematical model that is composed of a system of four-coupled nonlinear ordinary differential equations (page 518 in [1]) and that describes the action potential regeneration of the squid giant axon and the biophysical mechanisms underlying the action potential generation. Various types of mathematical models describing the electrical excitability of neurons and endocrine cells have been developed on the. T. Shirahata basis of the concepts proposed by Hodgkin and Huxley [1], and analyses of these models, including the RPeD1 neuron model in [2], various bursting models in Chapter 5 of [3], and pituitary lactotroph bursting model in [4], are important research areas in the field of applied mathematics. The concepts proposed by Hodgkin and Huxley [1] are important in the fields of theoretical physics [5] and mathematical physics [6]. The Hodgkin-Huxley model is used in drug-disease modeling (see Chapter 5.2.2 in [7])
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