Abstract
We investigate the response characteristics of a two-dimensional neuron model exposed to an externally applied extremely low frequency (ELF) sinusoidal electric field and the synchronization of neurons weakly coupled with gap junction. We find, by numerical simulations, that neurons can exhibit different spiking patterns, which are well observed in the structure of the recurrence plot (RP). We further study the synchronization between weakly coupled neurons in chaotic regimes under the influence of a weak ELF electric field. In general, detecting the phases of chaotic spiky signals is not easy by using standard methods. Recurrence analysis provides a reliable tool for defining phases even for noncoherent regimes or spiky signals. Recurrence-based synchronization analysis reveals that, even in the range of weak coupling, phase synchronization of the coupled neurons occurs and, by adding an ELF electric field, this synchronization increases depending on the amplitude of the externally applied ELF electric field. We further suggest a novel measure for RP-based phase synchronization analysis, which better takes into account the probabilities of recurrences.
Highlights
Action potentials, or spikes, are responsible for the transmission of information through the nervous system [1]
Using recurrence plot-based time series analysis, we investigate how the applied electric field (EF) affects the condition of synchronization of the coupled neurons
We suggest a slight modification of the recurrence-based phase synchronization measure
Summary
Spikes, are responsible for the transmission of information through the nervous system [1]. RPs can differentiate the stochastic and deterministic dynamics of irregularly firing cortical neurons [43] and show the average dynamics within a network of synchronized neurons [44] or spontaneous activity in neuronal in vitro cultures [45] They are powerful tools to study inter-relationships, coupling directions, phase synchronization, and Entropy 2022, 24, 235 generalized synchronization [34,46,47,48] and have been applied in different fields, such as chemistry, engineering, physiology, financial markets, and climatology [41,49,50,51,52,53]. We assume that the synaptic input current istim = 0 in order to study the response of a cortical neuron model exposed to an external sinusoidal field. Throughout this paper, we use the same parameter values for the ML model as explained in Table 1 [62]
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