Abstract
We introduce a new map-based neuron model derived from the dynamical perceptron family that has the best compromise between computational efficiency, analytical tractability, reduced parameter space and many dynamical behaviors. We calculate bifurcation and phase diagrams analytically and computationally that underpins a rich repertoire of autonomous and excitable dynamical behaviors. We report the existence of a new regime of cardiac spikes corresponding to nonchaotic aperiodic behavior. We compare the features of our model to standard neuron models currently available in the literature.
Highlights
Modeling the brain is not a simple task
We studied a model of action potential generation using difference equations obtained through the first order Taylor approximation of the hyperbolic tangent KTz neuron model [11]
We presented detailed bifurcation diagrams and fixed point stability diagrams for our new model, the so-called KTzLog neuron
Summary
Modeling the brain is not a simple task. Usually scientists opt for simple models that provide insights about the original phenomenon one is trying to study. Dynamics of an efficient map-based neuron model of the neuron membrane potential [9,10,11,12,13,14,15,16]. A whole class of map-based neuronal models derived from the classical McCulloch-Pitts perceptron [19] has been described [8] It consists of building up neuron models with recurrent dynamics from the simple perceptron until the desired dynamical complexity is reached. Using simple models of KTz family could facilitate the mathematical understanding of phenomena such as burst induced by subthreshold oscillations, cardiac arrhythmia or early afterdepolarization both studied in vitro and in vivo [23,24,25] or using conductance-based neurons [23, 25,26,27,28] which have huge parameter spaces. KTz family and conductance-based models have such a similar way of coupling neurons that our map-based neurons would allow the study of compartmental neurons
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