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Bifurcation analysis for Hindmarsh-Rose neuronal model with time-delayed feedback control and application to chaos control

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Science China(Technological Sciences) 2014年第5期57卷 872-878页

作者： WANG HaiXia WANG QingYun ZHENG YanHong School of Science Nanjing University of Science and Technology Department of Dynamics and Control Beihang University School of Mathematics and Computer Science Fujian Normal University

This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback *** stability and bifurcation analysis,we find that the excitable neuron can emit spikes via the subcritical Hopf bifurcation,and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external *** the purpose of control of chaos,we adopt the time-delayed feedback control,and convert chaos control to the Hopf bifurcation of the delayed feedback *** the analytical conditions under which the Hopf bifurcation occurs are given with an explicit *** on this,we show the Hopf bifurcation curves in the two-parameter ***,some numerical simulations are carried out to support the theoretical *** is shown that by appropriate choice of feedback gain and time delay,the chaotic orbit can be controlled to be *** adopted method in this paper is general and can be applied to other neuronal *** may help us better understand the bifurcation mechanisms of neural behaviors.

关键词： hopf bifurcation time-delayed feedback control chaos control neuronal model

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ASimplified neuronal model for the Instigation and Propagation of Cortical Spreading Depression

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Advances in Applied Mathematics and Mechanics 2011年第6期3卷 759-773页

作者： Huaxiong Huang Robert M.Miura Wei Yao Department of Mathematics and Statistics York UniversityTorontoOntario M3J1P3Canada Center for Applied Mathematics and Statistics New Jersey Institute of TechnologyNewarkNJ 07102USA Department of Mathematical Sciences New Jersey Institute of TechnologyNewarkNJ 07102USA Department of Mechanics and Engineering Science Fudan UniversityShanghai 200433China

In this paper,we construct a simplified neuronal model that is capable of simulating the instigation of cortical spreading depression(CSD)and propagation of a CSD *** model is a simplification and extension of a single neuron model proposed in the literature for studying the instigation of *** the simplified neuronal model,we construct a network of these simplified *** network model shows that the propagation of a CSD wave occurs naturally after it is instigated electrically or *** the model is simple,the speed of the CSD wave predicted by our model is consistent with experimentally observed ***,our model allows us to investigate the effects of specific ion channels on the spread of a CSD wave.

关键词： Cortical spreading depression neuronal model network numerical simulation

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Dynamics and synchronization of neural models with memristive membranes under energy coupling

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Chinese Physics B 2024年第5期33卷 316-322页

作者：万婧玥吴富强马军汪文帅 School of Mathematics and Statistics Ningxia UniversityYinchuan 750021China Ningxia Basic Science Research Center of Mathematics Ningxia UniversityYinchuan 750021China Department of Physics Lanzhou University of TechnologyLanzhou 730050China

Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical *** electrophysiological environment inside and outside of the nerve cell is *** to the continuous and periodical properties of electromagnetic fields in the cell during its operation,electronic components involving two capacitors and a memristor are effective in mimicking these physical *** this paper,a neural circuit is reconstructed by two capacitors connected by a memristor with periodical *** is found that the memristive neural circuit can present abundant firing patterns without *** Hamilton energy function is deduced using the Helmholtz ***,a neuronal network consisting of memristive neurons is proposed by introducing energy *** controllability and flexibility of parameters give the model the ability to describe the dynamics and synchronization behavior of the system.

关键词： memristor neuronal model energy synchronization

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Mathematical modeling of the biphasic dopaminergic response to glucose

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Journal of Biomedical Science and Engineering 2011年第2期4卷 136-145页

作者： Matthias Chung Britta Gobel Achim Peters Kerstin M.Oltmanns Andreas Moser Department of Mathematics Texas State UniversitySan MarcosUSA Institute of Mathematics and Image Computing Graduate School for Computing in Medicine and Life SciencesUniversity of LubeckLubeckGermany Medical Clinic I University of LubeckLubeckGermany Department of Psychiatry and Psychotherapy University of LubeckLubeckGermany Department of Neurology University of LubeckLubeckGermany

In this work, we specify potential elements of the brain to sense and regulate the energy metabolism of the organism. Our numerical investigations base on neurochemical experiments demonstrating a biphasic association between brain glucose level and neuronal activity. The dynamics of high and low affine KATP channels are most likely to play a decisive role in neuronal activity. We develop a coupled Hodgkin-Huxley model describing the interactive behavior of inhibitory GABAergic and excitatory dopaminergic neurons projecting into the caudate nucleus. The novelty in our approach is that we include the synaptic coupling of GABAergic and dopaminergic neurons as well as the interaction of high and low affine KATP channels. Both are crucial mechanisms described by kinetic models. Simulations demonstrate that our new model is coherent with neurochemical in vitro experiments. Even experimental interventions with glibenclamide and glucosamine are reproduced by our new model. Our results show that the considered dynamics of high and low affine KATP channels may be a driving force in energy sensing and global regulation of the energy metabolism, which supports central aspects of the new Selfish Brain Theory. Moreover, our simulations suggest that firing frequencies and patterns of GABAergic and dopaminergic neurons are correlated to their neurochemical outflow.

关键词： neuronal model Coupled Neurons Dopamine GABA K-ATP Channels Biphasic Glibenclamide Glucosamine

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Evoked-bursting from injured dorsal root ganglion neurons might act as a tactile allodynia pain signal

Evoked-bursting from injured dorsal root ganglion neurons mi...

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中国神经科学学会第九届全国学术会议暨第五次会员代表大会

作者： Ying SONG~(1,2),Hui-Ming LI~1,Zhi-Feng YUE~1,Rou-Gang XIE~1,Xue-Jun SONG~3,San-Jue HU~(1,*),Jun-Ling XING~(1,*) 1 Institute of Neuroscience,Fourth Military Medical University,17 Chang-Le West Road,Xi’an,710033,China 2 Department of Physiology,School of Anesthesiology and Jiangsu Province Key Laboratory of Anesthesiology,Xuzhou Medical College,Xuzhou,221000,China 3 Department of Neurobiology,Parker University Research Institute,2500 Walnut Hill Lane,Dallas,Texas,75229,USA

Objective Tactile allodynia is one of the common features of peripheral neuropathy in which myelinated Aβfibers were proven to have contributed to the behavior in animal models and patients in previous *** firing patterns have been observed in Aβfibers,though the specific firing pattern which might mediate tactile allodynia remains poorly understood.A kind of evoked-bursting(EB) was identified on Aβneurons on a neuropathic pain model, the present study is to explore the characteristics of EB,whether there are causal link between EB and allodynia,and also the ion mechanism underlying the *** Chronic compression of dorsal root ganglion(DRG) models (CCD model) were prepared for tactile allodynia *** vivo intracellular recording,extracellular recording and in vitro patch-clamp recording were used for the observation of activity of DRG neurons and wide dynamic range (WDR) *** In CCD models,dominant tactile allodynia could be *** DRG soma became hyperexcitable with various firing patterns,in which,EB(a periphery input spike followed by the somatic burst firing) was identified on Aβneurons with a significantly increased percentage of 43.3%compared to normal neurons (13.3%).Similar with spontaneous-bursting,a frequently observed firing pattern,the duration of EB increased with the membrane potential depolarization,and the existence of EB relied on the membrane potential oscillation.A distinct feature of EB is its dependence on periphery input especially from Aβafferent,which should be a prerequisite for the production of tactile ***-discharge of spinal cord WDR neurons in response to peripheral Aβstrength stimulation was a distinguishing feature of spinal neural correlate of tactile *** response was suppressed after abolishing EB at DRG level,thus,we propose that EB from injured DRG neurons might act as a tactile allodynia pain *** further investigated the ion current mechanism underlying *** c

关键词： dorsal root ganglion tactile allodynia wide dynamic range neuron evoked-bursting neuronal model

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