Responses to complex novel stimuli can be predicted by a simple neuron model of spike generation

Abstract Several hybrid neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. As one of the hybrid spiking neuron models, Izhikevich neuron model can reproduce major spike patterns observed in the cerebral cortex only by tuning a few parameters and also exhibit chaotic states in specific conditions. However, there are a few studies concerning the chaotic states over a large range of parameters due to the difficulty of dealing with the state dependent jump on the resetting process in this model. In this study, we examine the dependence of the system behavior on the resetting parameters by using Lyapunov exponent with saltation matrix and Poincaré section methods, and classify the routes to chaos.

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Analytical solution of linearized equations of the Morris-Lecar neuron model at large constant stimulation

10.1101/869875 ◽

2019 ◽

Author(s):

A.V. Paraskevov ◽

T.S. Zemskova

Keyword(s):

Neuron Model ◽

Neuronal Excitability ◽

Finite Interval ◽

Spike Generation ◽

Linearized Equations ◽

Spike Amplitude ◽

Model Equations ◽

Applicability Boundary ◽

Upper Boundary ◽

Stimulation Of

AbstractThe classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic spike generation occurs. Above the upper boundary of this interval there is a four-stage damping of the spike amplitude: 1) minor primary damping, which reflects a typical transient to stationary state, 2) plateau of nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a constant stationary asymptotic value Vst of the neuron potential. We have linearized the Morris-Lecar model equations at the vicinity of Vst and have shown that the linearized equations can be reduced to a standard equation for exponentially damped harmonic oscillations. Importantly, all coefficients of this equation can be explicitly expressed through parameters of the original Morris-Lecar model, enabling direct comparison (i.e. without any fitting) of the numerical and analytical solutions for the neuron potential dynamics at later stages of the spike amplitude damping. This allows to explore quantitatively the applicability boundary of linear stability analysis that implies exponential damping.

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Solution Methods for a New Class of Simple Model Neurons

Neural Computation ◽

10.1162/neco.2007.19.12.3216 ◽

2007 ◽

Vol 19 (12) ◽

pp. 3216-3225 ◽

Cited By ~ 4

Author(s):

Mark D. Humphries ◽

Kevin Gurney

Keyword(s):

Simple Model ◽

Neuron Model ◽

Solution Method ◽

Cortical Cell ◽

Spike Generation ◽

Firing Patterns ◽

New Class ◽

Efficient Simulation ◽

Different Types ◽

Solution Methods

Izhikevich (2003) proposed a new canonical neuron model of spike generation. The model was surprisingly simple yet able to accurately replicate the firing patterns of different types of cortical cell. Here, we derive a solution method that allows efficient simulation of the model.

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