With the help of a magnetic flux variable, the effects of stochastic electromagnetic disturbances on autapse Hodgkin-Huxley neuronal systems are studied systematically. Firstly, owing to the autaptic function, the inter-spike interval series of an autapse neuron not only bifurcates, but also presents a quasi-periodic characteristic. Secondly, an irregular mixed-mode oscillation induced by a specific electromagnetic disturbance is analyzed using the coefficient of variation of inter-spike intervals. It is shown that the neuronal discharge activity has certain selectivity to the noise intensity, and the appropriate noise intensity can induce the significant mixed-mode oscillations. Finally, the modulation effects of electromagnetic disturbances on a ring field-coupled neuronal network with autaptic structures are explored quantitatively using the average spiking frequency and the average coefficient of variation. The electromagnetic disturbances can not only destroy the continuous and synchronous discharge state, but also induce the resting neurons to generate the intermittent discharge mode and realize the transmission of neural signals in the neuronal network. The studies can provide some theoretical guidance for applying electromagnetic disturbances to effectively control the propagation of neural signals and treat mental illness.
To explore the feasibility of physiological manipulation of autaptic structures, the effects of autaptic connections on an FHN-ML neuronal system with phase noise stimulation are studied systematically. Firstly, according to the dynamic analysis of the FHN-ML neuron model, a saddle-node bifurcation can occur on an invariant circle. Under the action of external oscillatory current with phase noise, the neuronal firing activity is sensitive to phase noise with less intensity, and an appropriate noise intensity can induce a significant stochastic resonance phenomenon. Secondly, the chemical autaptic function can effectively regulate the neuronal discharge activity. An inhibitory autapse can not only induce the transition from depolarized resting to periodic spiking, but can also induce the FHN-ML neuron suppressed by strong phase noise to generate a pronounced intermittent high-level burst-like discharge mode when the autaptic conductance is greater than 0.1. Finally, for a two-dimensional regular FHN-ML neuronal network, a small amount of autaptic structures can induce some special waveforms to restore the propagation of nerve impulses interrupted by phase noise disturbance. This indicates the significant regulation of autapses on spatial patterns of the FHN-ML neuronal network. The study can provide some theoretical guidance for building autaptic structures in local areas to modulate the dynamic behaviors of biological neuronal systems.
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