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Breakup of Spiral Waves in Coupled hindmarsh-rose neurons

Chinese Physics Letters 2008年第12期25卷 4325-4328页

作者：马军贾亚唐军杨利建 Department of Physics Central China Normal University Wuhan 430079 School of Sciences Lanzhou University of Technology Lanzhou 730050

Breakup of spiral wave in the hindmarsh-rose neurons with nearest-neighbour couplings is reported. Appropriate initial values and parameter regions are selected to develop a stable spiral wave and then the Gaussian coloured noise with different intensities and correlation times is imposed on all neurons to study the breakup of spiral wave, respectively. Based on the mean field theory, the statistical factor of synchronization is defined to analyse the evolution of spiral wave. It is found that the stable rotating spiral wave encounters breakup with increasing intensity of Gaussian coloured noise or decreasing correlation time to certain threshold.

关键词： Spiral Wave hindmarsh-rose neuron

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Coherence resonance and synchronization of hindmarsh-rose neurons with noise

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Chinese Physics B 2005年第6期14卷 1088-1094页

作者：石霞陆启韶 SchoolofScience BeijingUniversityofAeronauticsandAstronauticsBeijing100083China

Noise effects on coherence resonance and synchronization of hindmarsh-rose (HR) neuron model are studied. The coherence resonance of a single HR neuron with Gaussian white noise added to the membrane potential is investigated in situations before, near and after the Hopf bifurcation, separately, with the external direct current as a bifurcation parameter. It is shown that even though there is no coupling between neurons, uncoupled identical HR neurons driven by a common noise can achieve complete synchronization when the noise intensity is higher than a critical value. Furthermore, noise also enhances complete synchronization of weakly coupled neurons. It is concluded that synchronization in bursting neurons is easier to be induced than in spiking ones, and coupling enhances the sensitivity of synchronization of neurons to noise stimulus.

关键词： coherence resonance synchronization hindmarsh-rose neuron Gaussian white noise

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Firing patterns and complete synchronization of coupled hindmarsh-rose neurons

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Chinese Physics B 2005年第1期14卷 77-85页

作者：石霞陆启韶 SchoolofScience BeijingUniversityofAeronauticsandAstronauticsBeijing100083China

The firing activities of hindmarsh-rose (HR) neurons are studied by means of numerical simulation and bifurcation analysis. A single HR neuron exhibits various firing patterns, such as quiescent state, periodic spiking, periodic bursting and chaos, when the external current input is changed. The fast/slow dynamical analysis is applied to explore the dynamical behaviour of the HR model. The complete synchronization of two coupled identical HR neurons with electrical coupling mimicking gap junctions can be realized in certain ranges of the coupling strength, whenever each individual neuron shows quiescency, periodic firing and chaos. The criteria for complete synchronization are analysed theoretically, and the corresponding numericaI simulation is presented as well. The persistence of the interspike intervals bifurcation structure of the coupled HR neuronal system under electrical coupling is also discussed.

关键词： hindmarsh-rose neuron synchronization coupling gap junction

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Multiple discharge modes and energy dependence of a 4-D neuron under periodic disturbance

Multiple discharge modes and energy dependence of a 4-D neur...

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第四届全国神经动力学学术会议

作者：史雪荣王作雷 School of Mathematics and Statistics Yancheng Teachers University

Based on hindmarsh-rose neuron, a 4-D neuron model is addressed. Various discharge modes of the proposed neuron model are investigated with the change of external disturbance. The diversity of electric activities of the neuron is to be revealed by altering the parameters in the external forcing current. According to Helmholtz theorem, Hamilton energy is calculated to describe the relationship between the energy and the discharge mode of the neuron. It is found that the energy is closely to the mode of electric activities caused by the change of the external forcing current and smaller energy occurs under bursting states. An interesting phenomenon is also found that the Hamilton energy is delayed by external forcing current, which means that the neuron plays an important role in energy coding. These research results may be beneficial for further exploring the dynamic behaviors relative to the mode transition of neuron network.

关键词： hindmarsh-rose neuron Hamilton energy bursting state periodic disturbance

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