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Models of neurons play an essential role in computational neuroscience. They provide a virtual laboratory to analyze the different regimes in the electrical activities of a single neuron or a network of neurons. They help the neuroscientist to have a better look at the nervous system. Some researchers have claimed that the transition of the ions through the membrane may induce an electrical field. In this paper, a new neuronal model is investigated which considers the effect of the electrical field. The dynamical properties of this model are studied. Different dynamical analyses are carried out to this end: investigating the stability of the equilibria, observing state space and trajectories, obtaining bifurcation diagram and Lyapunov exponents’ diagram, and finally exploring the basin of attraction.
Bo Yan; Shirin Panahi; Shaobo He; Sajad Jafari. Further dynamical analysis of modified Fitzhugh–Nagumo model under the electric field. Nonlinear Dynamics 2020, 101, 521 -529.
AMA StyleBo Yan, Shirin Panahi, Shaobo He, Sajad Jafari. Further dynamical analysis of modified Fitzhugh–Nagumo model under the electric field. Nonlinear Dynamics. 2020; 101 (1):521-529.
Chicago/Turabian StyleBo Yan; Shirin Panahi; Shaobo He; Sajad Jafari. 2020. "Further dynamical analysis of modified Fitzhugh–Nagumo model under the electric field." Nonlinear Dynamics 101, no. 1: 521-529.
Measuring the complexity of time series provides an important indicator for characteristic analysis of nonlinear systems. The permutation entropy (PE) is widely used, but it still needs to be modified. In this paper, the PE algorithm is improved by introducing the concept of the network, and the network PE (NPE) is proposed. The connections are established based on both the patterns and weights of the reconstructed vectors. The complexity of different chaotic systems is analyzed. As with the PE algorithm, the NPE algorithm-based analysis results are also reliable for chaotic systems. Finally, the NPE is applied to estimate the complexity of EEG signals of normal healthy persons and epileptic patients. It is shown that the normal healthy persons have the largest NPE values, while the EEG signals of epileptic patients are lower during both seizure-free intervals and seizure activity. Hence, NPE could be used as an alternative to PE for the nonlinear characteristics of chaotic systems and EEG signal-based physiological and biomedical analysis.
Bo Yan; Shaobo He; Kehui Sun. Design of a Network Permutation Entropy and Its Applications for Chaotic Time Series and EEG Signals. Entropy 2019, 21, 849 .
AMA StyleBo Yan, Shaobo He, Kehui Sun. Design of a Network Permutation Entropy and Its Applications for Chaotic Time Series and EEG Signals. Entropy. 2019; 21 (9):849.
Chicago/Turabian StyleBo Yan; Shaobo He; Kehui Sun. 2019. "Design of a Network Permutation Entropy and Its Applications for Chaotic Time Series and EEG Signals." Entropy 21, no. 9: 849.