Unidirectional synchronization of Hodgkin–Huxley neurons

Cornejo-Pérez, O.; Femat, R.

doi:10.1016/j.chaos.2004.10.006

Cited by 45 publications

(31 citation statements)

References 25 publications

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“…It is generally believed that there are two ways for synchronizing the system: self-synchronization caused by natural coupling with feedback from various synapses between neurons, and control synchronization, caused by the coupling effect generated by an artificial system applying explicit feedback control [10]. In the first case, synchronization of the coupling neurons of the same type only occurs when a certain critical value of the coupling strength is reached, and this value exceeds the physiological condition of time [11].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Chemical Synaptic Coupling of the Chay Neuron System under Time Delay

Wang

et al. 2018

Applied Sciences

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This paper studies the chemical synaptic coupling of Chay neurons and the effect of adding time delay on their synchronization behavior. The results indicate that coupling strength stimuli can affect the discharge activity and the synchronization behavior. In the absence of coupling strength, the Chay neurons have chaotic discharge behavior and the system is in a nonsynchronous state. When a certain coupling strength is added, the neurons change from chaotic discharge to ordered periodic discharge, and the system state changes from asynchronous to synchronous. On the other hand, a time lag can alter the coupled system from synchronous to asynchronous.

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Section: Introductionmentioning

confidence: 99%

Synchronization of Chemical Synaptic Coupling of the Chay Neuron System under Time Delay

Wang

et al. 2018

Applied Sciences

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“…Bin et al [25] introduced a backstepping control approach based on a Lyapunov function that achieves synchronization despite external disturbances. Based on feedback linearization ideas, Cornejo-Pérez and Femat [26] and Wang et al [27,28] introduced nonlinear controllers that achieve synchronization of coupled neurons despite external disturbances and unmeasured states. Nguyen and Hong [29] designed nonlinear and linear controllers with parameter adaptation to consider parameter uncertainties.…”

Section: Introductionmentioning

confidence: 99%

“…Synchronization approaches in neuronal systems are aimed at exploring the communication between neurons with the computing of coupling functions that resemble observed experimental electrical cell activity [6][7][8][9][10]. From the general synchronization point of view, synchronization approaches can be classified into two general groups [11,12]: (i) natural coupling (self-synchronization) [13][14][15][16][17][18][19][20][21] and (ii) artificial coupling using state observers or feedback control approaches [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

“…From control engineering, two ways for synchronization of nonlinear systems, including the case of neuronal systems, are (i) observer-based synchronization [11,12,22], which uses state observers to synchronize nonlinear oscillators with the same order and structure, reaching identical synchronization, and (ii) controller-based synchronization [23][24][25][26][27][28][29][30][31][32][33][34], which uses control laws to achieve the synchronization between nonlinear oscillators, with different structure and order.…”

Section: Introductionmentioning

confidence: 99%

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Robust Master‐Slave Synchronization of Neuronal Systems

Puebla

Hernández‐Martínez

Rodriguez-Jara

et al. 2017

Mathematical Problems in Engineering

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The desire to understand physiological mechanisms of neuronal systems has led to the introduction of engineering concepts to explain how the brain works. The synchronization of neurons is a central topic in understanding the behavior of living organisms in neurosciences and has been addressed using concepts from control engineering. We introduce a simple and reliable robust synchronization approach for neuronal systems. The proposed synchronization method is based on a master-slave configuration in conjunction with a coupling input enhanced with compensation of model uncertainties. Our approach has two nice features for the synchronization of neuronal systems: (i) a simple structure that uses the minimum information and (ii) good robustness properties against model uncertainties and noise. Two benchmark neuronal systems, Hodgkin-Huxley and Hindmarsh-Rose neurons, are used to illustrate our findings. The proposed synchronization approach is aimed at gaining insight into the effect of external electrical stimulation of nerve cells.

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“…A variety of quantitative analyses, control, and synchronization studies have been carried out. For instance, according to HH neuron model, accurate feedback [7] has been applied to realize the discharging synchronization between two HH neurons; under assumptions that all states are available, nonlinear control is proposed [8], additionally, when only membrane potential is available, linear adaptive control has also been designed to realize the discharging synchronization of HR neurons [8]; when system states and model are known, stable feedback control [9] based on Lyapunov stability theory has been designed and the synchronization of FitzHugh-Nagumo (FHN) neurons is achieved; adaptive neural network H ∞ approach proposed in [10] is utilized to synchronize two Ghostburster neurons. …”

Section: Introductionmentioning

confidence: 99%

Active Disturbance Rejection Synchronization of Morris‐Lecar Neurons

2018

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Synchronization of biological neurons is not only a hot topic, but also a difficult issue in the field of bioelectrical physiology. Numerous reported synchronization algorithms are designed on the basis of neural model, but they have deficiencies like relatively complex and poor robustness and are difficult to be realized. Morris-Lecar neuron is considered, and linear active disturbance rejection control (LADRC) is designed. Only one control input signal is utilized to synchronize membrane potentials of biological neurons. Meanwhile, in order to verify the robustness of synchronization, sinusoidal signal and parameter perturbations are introduced in numerical simulations. LADRC can still achieve satisfactory synchronization. Both theoretical and numerical simulation results show that LADRC is capable of estimating and cancelling disturbances and uncertainties. Neither accurate neural models nor concrete disturbance signal models are indispensable. A more practical and effective thought is provided to address the synchronization between neurons.

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Unidirectional synchronization of Hodgkin–Huxley neurons

Cited by 45 publications

References 25 publications

Synchronization of Chemical Synaptic Coupling of the Chay Neuron System under Time Delay

Synchronization of Chemical Synaptic Coupling of the Chay Neuron System under Time Delay

Robust Master‐Slave Synchronization of Neuronal Systems

Active Disturbance Rejection Synchronization of Morris‐Lecar Neurons

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