Dynamical response of a neuron–astrocyte coupling system under electromagnetic induction and external stimulation*

Yuan, Zhixuan; Feng, Peihua; Du, Mengmeng; Wu, Ying

doi:10.1088/1674-1056/ab7441

Cited by 23 publications

(7 citation statements)

References 56 publications

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“…It has been shown that fluctuations in the membrane potential of neurons can have a significant impact on the distribution of electromagnetic fields, causing changes in magnetic flux and electromagnetic induction across the cell membrane [ 38 , 39 ]. Therefore, it is crucial to consider the effect of electromagnetic induction on neuronal activity in the model.…”

Section: Numerical Resultsmentioning

confidence: 99%

Dynamic effect of electromagnetic induction on epileptic waveform

et al. 2022

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Background Electromagnetic induction has recently been considered as an important factor affecting the activity of neurons. However, as an important form of intervention in epilepsy treatment, few people have linked the two, especially the related dynamic mechanisms have not been explained clearly. Methods Considering that electromagnetic induction has some brain area dependence, we proposed a modified two-compartment cortical thalamus model and set eight different key bifurcation parameters to study the transition mechanisms of epilepsy. We compared and analyzed the application and getting rid of memristors of single-compartment and coupled models. In particular, we plotted bifurcation diagrams to analyze the dynamic mechanisms behind abundant discharge activities, which mainly involved Hopf bifurcations (HB), fold of cycle bifurcations (LPC) and torus bifurcations (TR). Results The results show that the coupled model can trigger more discharge states due to the driving effect between compartments. Moreover, the most remarkable finding of this study is that the memristor shows two sides. On the one hand, it may reduce tonic discharges. On the other hand, it may cause new pathological states. Conclusions The work explains the control effect of memristors on different brain regions and lays a theoretical foundation for future targeted therapy. Finally, it is hoped that our findings will provide new insights into the role of electromagnetic induction in absence seizures.

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Section: Numerical Resultsmentioning

confidence: 99%

Dynamic effect of electromagnetic induction on epileptic waveform

et al. 2022

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“…In the literature, flux-controlled memristors were used in various neuron models to depict the dynamic relation between the membrane potential and magnetic flux [21]. In other words, the flux-controlled memristors were used in the Hodgkin-Huxley neuron model [22][23][24], Izhikevich neuron model [25], FitzHugh-Nagumo neuron model [26], and threedimensional (3D) [27][28][29][30][31]/two dimensional (2D) [32][33][34] Hindmarsh-Rose neuron model to depict the electromagnetic induction effect. These memristive neuron models can generate abundant firing patterns since the involvement of the flux-controlled memristor.…”

Section: Introductionmentioning

confidence: 99%

Hidden firing patterns and memristor initial condition-offset boosting behavior in a memristive Hindmarsh-Rose neuron model

et al. 2023

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Electromagnetic induction can effectively induce abundant firing patterns in neurons. In modeling a neuron model with the electromagnetic induction effect, an electromagnetic induction current is frequently added to the state equation of membrane potential. To more properly reflect the non-uniform distribution of the ions inside and outside the neuron membrane, an ideal flux-controlled memristor with sinusoidal memductance function and non-linearly modulated input is raised to depict an electromagnetic induction effect on a Hindmarsh–Rose neuron model, and thereby, a three-dimensional (3D) memristive Hindmarsh–Rose (mHR) neuron model is built in this paper. The proposed mHR neuron model possesses no equilibrium point since the involvement of the ideal flux-controlled memristor, which induces the generation of hidden dynamics. Numerical results declare that the mHR neuron model can generate abundant hidden dynamics, i.e., periodic spiking, chaotic spiking, period-doubling bifurcation route, tangent bifurcation, and chaos crisis. These hidden dynamics are much related to the memristor coupling strength and externally applied stimulus. Afterward, the memristor initial condition-offset boosting behavior is revealed. This can trigger the generation of infinite multiple coexisting firing patterns along the memristor variable coordinate. These coexisting firing patterns have identical attractor topology but different locations in the phase plane. Finally, an analog circuit is designed for implementing the mHR neuron model, and PSIM-based circuit simulation is executed. The circuit-simulated results perfectly verify the generation of hidden infinite multiple coexisting initial condition-offset boosting firing patterns in the proposed mHR neuron model.

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“…[15,16] That is to say, the neuron can realize its functions by feeling externally applied stimulus and conduc-tion excitation of the change electrophysiology. [17,18] To date, many explorations have revealed that externally applied stimulus and electromagnetic induction influence the dynamical properties of neuron electrical activities. By introducing an external applied current into HR model, various types of coexisting asymmetric bursters were disclosed.…”

Section: Introductionmentioning

confidence: 99%

Continuous non-autonomous memristive Rulkov model with extreme multistability*

Liu

Feng

et al. 2021

Chinese Phys. B

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Based on the two-dimensional (2D) discrete Rulkov model that is used to describe neuron dynamics, this paper presents a continuous non-autonomous memristive Rulkov model. The effects of electromagnetic induction and external stimulus are simultaneously considered herein. The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current. Thus, the presented model possesses a line equilibrium set evolving over the time. The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed. Afterwards, numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction, external stimulus, and initial conditions. Interestingly, the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model. Furthermore, an analog circuit of the proposed model is implemented, upon which the hardware experiment is executed to verify the numerically simulated extreme multistability. The extreme multistability is numerically revealed and experimentally confirmed in this paper, which can widen the future engineering employment of the Rulkov model.

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Dynamical response of a neuron–astrocyte coupling system under electromagnetic induction and external stimulation*

Cited by 23 publications

References 56 publications

Dynamic effect of electromagnetic induction on epileptic waveform

Dynamic effect of electromagnetic induction on epileptic waveform

Hidden firing patterns and memristor initial condition-offset boosting behavior in a memristive Hindmarsh-Rose neuron model

Continuous non-autonomous memristive Rulkov model with extreme multistability*

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