The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statisti...The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.展开更多
Logical resonance has been demonstrated to be present in the Fitz Hugh-Nagumo(FHN)neuron,namely,the FHN neuron can operate as a reliable logic gate within an optimal parameter window.Here we attempt to extend the resu...Logical resonance has been demonstrated to be present in the Fitz Hugh-Nagumo(FHN)neuron,namely,the FHN neuron can operate as a reliable logic gate within an optimal parameter window.Here we attempt to extend the results to the more biologically realistic Hodgkin-Huxley(HH)model of neurons.In general,biological organisms have an optimal temperature at which the biological functions are most effective.In view of this,we examine if there is an optimal range of temperature where the HH neuron can work like a specific logic gate,and how temperature influences the logical resonance.Here we use the success probability P to measure the reliability of the specific logic gate.For AND logic gate,P increases with temperature T,reaches the maximum in an optimal window of T,and eventually decreases,which indicates the occurrence of the temperature-induced logical resonance phenomenon in the HH neuron.Moreover,single and double logical resonances can be induced by altering the frequency of the modulating periodic signal under the proper temperatures,suggesting the appearance of temperature-controlled transition of logical resonance.These results provide important clues for constructing neuron-based energy-efficient new-fashioned logical devices.展开更多
The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise,higher-order compact numerical scheme that results in truly outstanding accuracy at a g...The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise,higher-order compact numerical scheme that results in truly outstanding accuracy at a given cost.The objective of this article is to develop a highly accurate novel algorithm for two dimensional non-linear Burgers Huxley(BH)equations.The proposed compact numerical scheme is found to be free of superiors approximate oscillations across discontinuities,and in a smooth ow region,it efciently obtained a high-order accuracy.In particular,two classes of higherorder compact nite difference schemes are taken into account and compared based on their computational economy.The stability and accuracy show that the schemes are unconditionally stable and accurate up to a two-order in time and to six-order in space.Moreover,algorithms and data tables illustrate the scheme efciency and decisiveness for solving such non-linear coupled system.Efciency is scaled in terms of L_(2) and L_(∞) norms,which validate the approximated results with the corresponding analytical solution.The investigation of the stability requirements of the implicit method applied in the algorithm was carried out.Reasonable agreement was constructed under indistinguishable computational conditions.The proposed methods can be implemented for real-world problems,originating in engineering and science.展开更多
Spiking regularity in a clustered Hodgkin–Huxley（HH） neuronal network has been studied in this letter. A stochastic HH neuronal model with channel blocks has been applied as local neuronal model. Effects of the int...Spiking regularity in a clustered Hodgkin–Huxley（HH） neuronal network has been studied in this letter. A stochastic HH neuronal model with channel blocks has been applied as local neuronal model. Effects of the internal channel noise on the spiking regularity are discussed by changing the membrane patch size. We find that when there is no channel blocks in potassium channels, there exist some intermediate membrane patch sizes at which the spiking regularity could reach to a higher level. Spiking regularity increases with the membrane patch size when sodium channels are not blocked. Namely, depending on different channel blocking states, internal channel noise tuned by membrane patch size could have different influence on the spiking regularity of neuronal networks.展开更多
The application of Sobolev gradient methods for finding critical points of the Huxley and Fisher models is demonstrated. A comparison is given between the Euclidean, weighted and unweighted Sobolev gradients. Results ...The application of Sobolev gradient methods for finding critical points of the Huxley and Fisher models is demonstrated. A comparison is given between the Euclidean, weighted and unweighted Sobolev gradients. Results are given for the one dimensional Huxley and Fisher models.展开更多
基金Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China(Grant No.11125419)the National Natural Science Foundation of China(Grant No.10925525)+1 种基金the Funds for the Leading Talents of Fujian ProvinceChina
文摘The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.
基金This Project supported by the National Natural Science Foundation of China (Grant No.11804111)。
文摘Logical resonance has been demonstrated to be present in the Fitz Hugh-Nagumo(FHN)neuron,namely,the FHN neuron can operate as a reliable logic gate within an optimal parameter window.Here we attempt to extend the results to the more biologically realistic Hodgkin-Huxley(HH)model of neurons.In general,biological organisms have an optimal temperature at which the biological functions are most effective.In view of this,we examine if there is an optimal range of temperature where the HH neuron can work like a specific logic gate,and how temperature influences the logical resonance.Here we use the success probability P to measure the reliability of the specific logic gate.For AND logic gate,P increases with temperature T,reaches the maximum in an optimal window of T,and eventually decreases,which indicates the occurrence of the temperature-induced logical resonance phenomenon in the HH neuron.Moreover,single and double logical resonances can be induced by altering the frequency of the modulating periodic signal under the proper temperatures,suggesting the appearance of temperature-controlled transition of logical resonance.These results provide important clues for constructing neuron-based energy-efficient new-fashioned logical devices.
文摘The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise,higher-order compact numerical scheme that results in truly outstanding accuracy at a given cost.The objective of this article is to develop a highly accurate novel algorithm for two dimensional non-linear Burgers Huxley(BH)equations.The proposed compact numerical scheme is found to be free of superiors approximate oscillations across discontinuities,and in a smooth ow region,it efciently obtained a high-order accuracy.In particular,two classes of higherorder compact nite difference schemes are taken into account and compared based on their computational economy.The stability and accuracy show that the schemes are unconditionally stable and accurate up to a two-order in time and to six-order in space.Moreover,algorithms and data tables illustrate the scheme efciency and decisiveness for solving such non-linear coupled system.Efciency is scaled in terms of L_(2) and L_(∞) norms,which validate the approximated results with the corresponding analytical solution.The investigation of the stability requirements of the implicit method applied in the algorithm was carried out.Reasonable agreement was constructed under indistinguishable computational conditions.The proposed methods can be implemented for real-world problems,originating in engineering and science.
基金supported by the National Natural Science Foundation of China(11102094 and 11272024)the Fundamental Research Funds for the Central University(2013RC0904)
文摘Spiking regularity in a clustered Hodgkin–Huxley（HH） neuronal network has been studied in this letter. A stochastic HH neuronal model with channel blocks has been applied as local neuronal model. Effects of the internal channel noise on the spiking regularity are discussed by changing the membrane patch size. We find that when there is no channel blocks in potassium channels, there exist some intermediate membrane patch sizes at which the spiking regularity could reach to a higher level. Spiking regularity increases with the membrane patch size when sodium channels are not blocked. Namely, depending on different channel blocking states, internal channel noise tuned by membrane patch size could have different influence on the spiking regularity of neuronal networks.
文摘The application of Sobolev gradient methods for finding critical points of the Huxley and Fisher models is demonstrated. A comparison is given between the Euclidean, weighted and unweighted Sobolev gradients. Results are given for the one dimensional Huxley and Fisher models.
