One dimensional map-based neuron model: A phase space interpretation

Abstract

Abstract Computational models play an essential role in studying and predicting the behavior of a bio-system. Discrete dynamical models, usually known as maps, are important, especially when it comes to the mathematical study of the behavior of the neurons and neural network. Map-based neural models are simple, yet powerful and computationally efficient tools to study complex dynamical systems. In this paper, a one-dimensional map-based neuron model is proposed for which various dynamical behaviors are investigated using phase-space interpretation. In order to reproduce the behaviors observed in the real neurons such as action potential (AP), spike, burst, chaotic burst and, myocardial AP, different multi-criteria functions are formulated. In our proposed model, all the mentioned dynamical behaviors can be obtained only by changing the respective parameter. Therefore, though being simple, in terms of both analytical solutions and numerical calculations, our model is perfectly capable of demonstrating complex behaviors. In this study, the response of the model to various stimuli (excitation current) is explored. The time series analysis, phase-space and cobweb plot are provided as well for each multi-criteria function. Also, the bifurcation analysis with respect to different parameters of the model is carried out.