Ionic channel blockage in stochastic Hodgkin–Huxley neuronal model driven by multiple oscillatory signals

Zhou, Xiuying; Xu, Ying; Wang, Guowei; Jia, Ya

doi:10.1007/s11571-020-09593-7

Cited by 35 publications

(12 citation statements)

References 65 publications

(79 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are a large number of flowing charged ions inside and outside the cell membrane [61,67]. Therefore, electromagnetic induction (EMI) effect can be introduced into Izhikevich neuronal model according to Faraday's law of electromagnetic induction [68].…”

Section: Izhikevich Neuron Model Under the Effects Of Emimentioning

confidence: 99%

Chaotic resonance in Izhikevich neural network motifs under electromagnetic induction

et al. 2022

Self Cite

View full text Add to dashboard Cite

Chaotic resonance (CR) is the response of a nonlinear system to weak signals enhanced by internal or external chaotic activity (such as the signal derived from Lorenz system). In this paper, the triple-neuron feed-forward loop (FFL) Izhikevich neural network motifs with eight types are constructed as the nonlinear systems, and the effects of EMI on CR phenomenon in FFL neuronal network motifs are studied. It is found that both the single Izhikevich neural model under electromagnetic induction (EMI) and its network motifs exhibit CR phenomenon depending on the chaotic current intensity. There exists an optimal chaotic current intensity ensuring the best detection of weak signal in single Izhikevich neuron or its network motifs via CR. The EMI can enhance the ability of neuron to detect weak signals. For T1-FFL and T2-FFL motifs, the adjustment of EMI parameters makes T2-FFL show a more obvious CR phenomenon than that for T1-FFL motifs, which is different from the impact of system parameters (e.g., the weak signal frequency, the coupling strength, and the time delay) on CR. Another interesting phenomenon is that the variation of CR with time delay exhibits quasi periodic characteristics. Our results showed that CR effect is a robust phenomenon which is observed in both single Izhikevich neuron and network motifs, which might help one understand how to improve the ability of weak signal detection and propagation in neuronal system.

show abstract

Section: Izhikevich Neuron Model Under the Effects Of Emimentioning

confidence: 99%

Chaotic resonance in Izhikevich neural network motifs under electromagnetic induction

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…The neurons are considered as basic units to form neural systems, which have received much interest because of the great significance and applications in neural science, brain science, medical technology, and so on. To simplify matters, the Hodgkin-Huxley (HH) equation [1][2][3] is usually used to investigate the dynamics of neural networks. Although the HH equation and its modified versions are simplification of dynamics of a realistic neuron, it is still complex in some problems.…”

Section: Introductionmentioning

confidence: 99%

The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method

Zhen

Song

2021

Neural Plasticity

View full text Add to dashboard Cite

The synchronization between two coupled FitzHugh-Nagumo (FHN) neurons with or without external current is studied by using the Laplace transform and the Adomian decomposition method. Different from other researches, the synchronization error system is expressed as sets of Volterra integral equations based on the convolution theorem in the Laplace transform. Then, it is easy to analytically obtain the conditions that synchronization errors disappear based on the successive approximation method in integral equation theorem, the correctness of which is verified by numerical simulations. Furthermore, the synchronous dynamics of the two coupled FHN neurons also can be written in the form of Volterra integral equations, which is more convenient to analytically solve by using the Adomian decomposition method. It is found that the occurrence of synchronization between the two FHN neurons only depends on the coupling strength and is irrelevant to the external current. Only synchronous rest state in the two FHN neurons without external current can be achieved, while synchronous spikes appear if the external current is not zero.

show abstract

“…The study of neurons plays a very important role in many applications in neural science, brain science, and so on. The famous Hodgkin-Huxley (HH) equation, proposed by Hodgkin and Huxley in 1952, [ 1 , 2 ] usually was used to construct neural systems or exhibit the neural dynamic behavior. Since then, other neuronal models, such as the FizHugh-Nagumo (FHN) model [ 3 ], the Hindmarsh-Rose (HR) model [ 4 ], the Chay model [ 5 ], and the Morris-Lecar model [ 6 ], also have been published.…”

Section: Introductionmentioning

confidence: 99%

A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method

Zhen

Song

2021

Neural Plasticity

View full text Add to dashboard Cite

In this paper, an analytical criterion is proposed to investigate the synchronization between two Hindmarsh-Rose neurons with linear and nonlinear coupling functions based on the Laplace transform method. Different from previous works, the synchronization error system is expressed in its integral form, which is more convenient to analyze. The synchronization problem of two HR coupled neurons is ultimately converted into the stability problem of roots to a nonlinear algebraic equation. Then, an analytical criterion for synchronization between the two HR neurons can be given by using the Routh-Hurwitz criterion. Numerical simulations show that the synchronization criterion derived in this paper is valid, regardless of the periodic spikes or burst-spike chaotic behavior of the two HR neurons. Furthermore, the analytical results have almost the same accuracy as the conditional Lyapunov method. In addition, the calculation quantities always are small no matter the linear and nonlinear coupling functions, which show that the approach presented in this paper is easy to be developed to study synchronization between a large number of HR neurons.

show abstract

Ionic channel blockage in stochastic Hodgkin–Huxley neuronal model driven by multiple oscillatory signals

Cited by 35 publications

References 65 publications

Chaotic resonance in Izhikevich neural network motifs under electromagnetic induction

Chaotic resonance in Izhikevich neural network motifs under electromagnetic induction

The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method

A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method

Contact Info

Product

Resources

About