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

This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By 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 current.For 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 system.Then the analytical conditions under which the Hopf bifurcation occurs are given with an explicit formula.Based on this,we show the Hopf bifurcation curves in the two-parameter plane.Finally,some numerical simulations are carried out to support the theoretical results.It is shown that by appropriate choice of feedback gain and time delay,the chaotic orbit can be controlled to be stable.The adopted method in this paper is general and can be applied to other neuronal models.It may help us better understand the bifurcation mechanisms of neural behaviors.

Advances in memristor based artificial neuron fabrication-materials,models,and applications

Spiking neural network(SNN),widely known as the third-generation neural network,has been frequently investigated due to its excellent spatiotemporal information processing capability,high biological plausibility,and low energy consumption characteristics.Analogous to the working mechanism of human brain,the SNN system transmits information through the spiking action of neurons.Therefore,artificial neurons are critical building blocks for constructing SNN in hardware.Memristors are drawing growing attention due to low consumption,high speed,and nonlinearity characteristics,which are recently introduced to mimic the functions of biological neurons.Researchers have proposed multifarious memristive materials including organic materials,inorganic materials,or even two-dimensional materials.Taking advantage of the unique electrical behavior of these materials,several neuron models are successfully implemented,such as Hodgkin–Huxley model,leaky integrate-and-fire model and integrate-and-fire model.In this review,the recent reports of artificial neurons based on memristive devices are discussed.In addition,we highlight the models and applications through combining artificial neuronal devices with sensors or other electronic devices.Finally,the future challenges and outlooks of memristor-based artificial neurons are discussed,and the development of hardware implementation of brain-like intelligence system based on SNN is also prospected.

Memristors-coupled neuron models with multiple firing patterns and homogeneous and heterogeneous multistability

Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons.In this paper,two distinct scenarios,i.e.,an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse,are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh-Rose neuron model.Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns.The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors.Finally,the simulation circuit and DSP hardware implementation results validate the physical mechanism,as well as the reliability of the biological neuron model.

A Novel Parallel Computing Confidentiality Scheme Based on Hindmarsh-Rose Model

Due to the inherent insecure nature of the Internet,it is crucial to ensure the secure transmission of image data over this network.Additionally,given the limitations of computers,it becomes evenmore important to employ efficient and fast image encryption techniques.While 1D chaotic maps offer a practical approach to real-time image encryption,their limited flexibility and increased vulnerability restrict their practical application.In this research,we have utilized a 3DHindmarsh-Rosemodel to construct a secure cryptosystem.The randomness of the chaotic map is assessed through standard analysis.The proposed system enhances security by incorporating an increased number of system parameters and a wide range of chaotic parameters,as well as ensuring a uniformdistribution of chaotic signals across the entire value space.Additionally,a fast image encryption technique utilizing the new chaotic system is proposed.The novelty of the approach is confirmed through time complexity analysis.To further strengthen the resistance against cryptanalysis attacks and differential attacks,the SHA-256 algorithm is employed for secure key generation.Experimental results through a number of parameters demonstrate the strong cryptographic performance of the proposed image encryption approach,highlighting its exceptional suitability for secure communication.Moreover,the security of the proposed scheme has been compared with stateof-the-art image encryption schemes,and all comparison metrics indicate the superior performance of the proposed scheme.

Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

The firing of a neuron model is mainly affected by the following factors:the magnetic field,external forcing current,time delay,etc.In this paper,a new time-delayed electromagnetic field coupled dual Hindmarsh-Rose neuron network model is constructed.A magnetically controlled threshold memristor is improved to represent the self-connected and the coupled magnetic fields triggered by the dynamic change of neuronal membrane potential for the adjacent neurons.Numerical simulation confirms that the coupled magnetic field can activate resting neurons to generate rich firing patterns,such as spiking firings,bursting firings,and chaotic firings,and enable neurons to generate larger firing amplitudes.The study also found that the strength of magnetic coupling in the neural network also affects the number of peaks in the discharge of bursting firing.Based on the existing medical treatment background of mental illness,the effects of time lag in the coupling process against neuron firing are studied.The results confirm that the neurons can respond well to external stimuli and coupled magnetic field with appropriate time delay,and keep periodic firing under a wide range of external forcing current.

Development and transition of spiral wave in the coupled Hindmarsh-Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh-Rose （H-R） neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D＇, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons （or sites） and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.

Instability and Death of Spiral Wave in a Two-Dimensional Array of Hindmarsh-Rose Neurons

Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriateparameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventriculartachycardia that can denervate into polymorphic tachycardia and ventricular fibrillation. The neuronal system oftenconsists of a large number of neurons with complex connections. In this paper, we theoretically study the transitionfrom spiral wave to spiral turbulence and homogeneous state (death of spiral wave) in two-dimensional array of theHindmarsh-Rose neuron with completely nearest-neighbor connections. In our numerical studies, a stable rotating spiralwave is developed and selected as the initial state, then the bifurcation parameters are changed to different values toobserve the transition from spiral wave to homogeneous state, breakup of spiral wave and weak change of spiral wave,respectively. A statistical factor of synchronization is defined with the mean field theory to analyze the transition fromspiral wave to other spatial states, and the snapshots of the membrane potentials of all neurons and time series of meanmembrane potentials of all neurons are also plotted to discuss the change of spiral wave. It is found that the sharpchanging points in the curve for factor of synchronization vs. bifurcation parameter indicate sudden transition fromspiral wave to other states. And the results are independent of the number of neurons we used.

Alleviated mucosal and neuronal damage in a rat model of Crohn's disease

AIM:To establish a rat model suitable to investigate the repetitive relapsing inflammations(RRI)characteristic to Crohn’s disease.METHODS:Colitis was induced by 2,4,6-trinitrobenzenesulfonic acid(TNBS).RRI were mimicked by repeating administrations of TNBS.Tissue samples were taken from control,once,twice and three times treated rats from the inflamed and adjacent non-inflamed colonic segments at different timepoints during the acute intestinal inflammation.The means of the ulcerated area were measured to evaluate the macroscopic mu-cosal damage.The density of myenteric neurons was determined on whole mounts by Hu C/Hu D immunohistochemistry.Heme oxygenase-1(HO-1)expression was evaluated by molecular biological techniques.RESULTS:TNBS-treated rats displayed severe colitis,but the mortality was negligible,and an increase of body weight was characteristic throughout the experimental period.The widespread loss of myenteric neurons,and marked but transient HO-1 up-regulation were demonstrated after the first TNBS administration.After repeated doses the length of the recovery time and extent of the ulcerous colonic segments were markedly decreased,and the neuronal loss was on a smaller scale and was limited to the inflamed area.HO-1 m RNA level was notably greater than after a single dose and overexpression was sustained throughout the timepoints examined.Nevertheless,the HO-1protein up-regulation after the second TNBS treatment proved to be transient.Following the third treatment HO-1 protein expression could not be detected.CONCLUSION:Experimentally provoked RRI may exert a protective preconditioning effect against the mucosal and neuronal damage.The persistent up-regulation of HO-1 m RNA expression may correlate with this.

Distinct neuronal excitability alterations of medial prefrontal cortex in early-life neglect model of rats

Object:Early-life neglect has irreversible emotional effects on the central nervous system.In this work,we aimed to elucidate distinct functional neural changes in me-dial prefrontal cortex(mPFC)of model rats.Methods:Maternal separation with early weaning was used as a rat model of early-life neglect.The excitation of glutamatergic and GABAergic neurons in rat mPFC was recorded and analyzed by whole-cell patch clamp.Results:Glutamatergic and GABAergic neurons of mPFC were distinguished by typi-cal electrophysiological properties.The excitation of mPFC glutamatergic neurons was significantly increased in male groups,while the excitation of mPFC GABAergic neurons was significant in both female and male groups,but mainly in terms of rest membrane potential and amplitude,respectively.Conclusions:Glutamatergic and GABAergic neurons in medial prefrontal cortex showed different excitability changes in a rat model of early-life neglect,which can contribute to distinct mechanisms for emotional and cognitive manifestations.

Serotonin controls axon and neuronal regeneration in the nervous system:lessons from regenerating animal models

Traumatic brain injury （TBI） is a mechanical injury to brain tissue that leads to an impairment of function and a broad spectrum of symptoms and disabilities; often, it is followed by diffuse axonal injury, which causes denaturation of the white matter and axon retraction, leaving patients with severe brain damage or even in a persistent vegetative state.

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

Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical mechanisms.The electrophysiological environment inside and outside of the nerve cell is different.Due 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 features.In this paper,a neural circuit is reconstructed by two capacitors connected by a memristor with periodical mem-conductance.It is found that the memristive neural circuit can present abundant firing patterns without stimulus.The Hamilton energy function is deduced using the Helmholtz theorem.Further,a neuronal network consisting of memristive neurons is proposed by introducing energy coupling.The controllability and flexibility of parameters give the model the ability to describe the dynamics and synchronization behavior of the system.

Exploiting fly models to investigate rare human neurological disorders

Rare neurological diseases,while individually are rare,collectively impact millions globally,leading to diverse and often severe neurological symptoms.Often attributed to genetic mutations that disrupt protein function or structure,understanding their genetic basis is crucial for accurate diagnosis and targeted therapies.To investigate the underlying pathogenesis of these conditions,researchers often use non-mammalian model organisms,such as Drosophila(fruit flies),which is valued for their genetic manipulability,cost-efficiency,and preservation of genes and biological functions across evolutionary time.Genetic tools available in Drosophila,including CRISPR-Cas9,offer a means to manipulate gene expression,allowing for a deep exploration of the genetic underpinnings of rare neurological diseases.Drosophila boasts a versatile genetic toolkit,rapid generation turnover,and ease of large-scale experimentation,making it an invaluable resource for identifying potential drug candidates.Researchers can expose flies carrying disease-associated mutations to various compounds,rapidly pinpointing promising therapeutic agents for further investigation in mammalian models and,ultimately,clinical trials.In this comprehensive review,we explore rare neurological diseases where fly research has significantly contributed to our understanding of their genetic basis,pathophysiology,and potential therapeutic implications.We discuss rare diseases associated with both neuron-expressed and glial-expressed genes.Specific cases include mutations in CDK19 resulting in epilepsy and developmental delay,mutations in TIAM1 leading to a neurodevelopmental disorder with seizures and language delay,and mutations in IRF2BPL causing seizures,a neurodevelopmental disorder with regression,loss of speech,and abnormal movements.And we explore mutations in EMC1 related to cerebellar atrophy,visual impairment,psychomotor retardation,and gain-of-function mutations in ACOX1 causing Mitchell syndrome.Loss-of-function mutations in ACOX1 result in ACOX1 deficiency,characterized by very-long-chain fatty acid accumulation and glial degeneration.Notably,this review highlights how modeling these diseases in Drosophila has provided valuable insights into their pathophysiology,offering a platform for the rapid identification of potential therapeutic interventions.Rare neurological diseases involve a wide range of expression systems,and sometimes common phenotypes can be found among different genes that cause abnormalities in neurons or glia.Furthermore,mutations within the same gene may result in varying functional outcomes,such as complete loss of function,partial loss of function,or gain-of-function mutations.The phenotypes observed in patients can differ significantly,underscoring the complexity of these conditions.In conclusion,Drosophila represents an indispensable and cost-effective tool for investigating rare neurological diseases.By facilitating the modeling of these conditions,Drosophila contributes to a deeper understanding of their genetic basis,pathophysiology,and potential therapies.This approach accelerates the discovery of promising drug candidates,ultimately benefiting patients affected by these complex and understudied diseases.

Reduced mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor contributes to neurodegeneration in a model of spinal and bulbar muscular atrophy pathology

Spinal and bulbar muscular atrophy is a neurodegenerative disease caused by extended CAG trinucleotide repeats in the androgen receptor gene,which encodes a ligand-dependent transcription facto r.The mutant androgen receptor protein,characterized by polyglutamine expansion,is prone to misfolding and forms aggregates in both the nucleus and cytoplasm in the brain in spinal and bulbar muscular atrophy patients.These aggregates alter protein-protein interactions and compromise transcriptional activity.In this study,we reported that in both cultured N2a cells and mouse brain,mutant androgen receptor with polyglutamine expansion causes reduced expression of mesencephalic astrocyte-de rived neurotrophic factor.Overexpressio n of mesencephalic astrocyte-derived neurotrophic factor amelio rated the neurotoxicity of mutant androgen receptor through the inhibition of mutant androgen receptor aggregation.Conversely.knocking down endogenous mesencephalic astrocyte-derived neurotrophic factor in the mouse brain exacerbated neuronal damage and mutant androgen receptor aggregation.Our findings suggest that inhibition of mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor is a potential mechanism underlying neurodegeneration in spinal and bulbar muscular atrophy.

The burden of upper motor neuron involvement is correlated with the bilateral limb involvement interval in patients with amyotrophic lateral sclerosis:a retrospective observational study

Amyotrophic lateral sclerosis is a rare neurodegenerative disease characterized by the involvement of both upper and lower motor neurons.Early bilateral limb involvement significantly affects patients'daily lives and may lead them to be confined to bed.However,the effect of upper and lower motor neuron impairment and other risk factors on bilateral limb involvement is unclear.To address this issue,we retrospectively collected data from 586 amyotrophic lateral sclerosis patients with limb onset diagnosed at Peking University Third Hospital between January 2020 and May 2022.A univariate analysis revealed no significant differences in the time intervals of spread in different directions between individuals with upper motor neuron-dominant amyotrophic lateral sclerosis and those with classic amyotrophic lateral sclerosis.We used causal directed acyclic graphs for risk factor determination and Cox proportional hazards models to investigate the association between the duration of bilateral limb involvement and clinical baseline characteristics in amyotrophic lateral sclerosis patients.Multiple factor analyses revealed that higher upper motor neuron scores(hazard ratio[HR]=1.05,95%confidence interval[CI]=1.01–1.09,P=0.018),onset in the left limb(HR=0.72,95%CI=0.58–0.89,P=0.002),and a horizontal pattern of progression(HR=0.46,95%CI=0.37–0.58,P<0.001)were risk factors for a shorter interval until bilateral limb involvement.The results demonstrated that a greater degree of upper motor neuron involvement might cause contralateral limb involvement to progress more quickly in limb-onset amyotrophic lateral sclerosis patients.These findings may improve the management of amyotrophic lateral sclerosis patients with limb onset and the prediction of patient prognosis.

From neurogenesis to neuronal regeneration: the amphibian olfactory system as a model to visualize neuronal development in vivo

How do individual neurons develop and how are they in- tegrated into neuronal circuitry？ To answer this question is essential to understand how the nervous system develops and how it is maintained during the adult life. A neural stem cell must go through several stages of maturation, including proliferation, migration, differentiation, and integration, to become fully embedded to an existing neuronal circuit. The knowledge on this topic so far has come mainly from cell culture studies. Studying the development of individual neurons within intact neuronal networks in vivo is inherently difficult. Most neurons are generated form neural stem cells during embryonic and early postnatal development.

Neuroactive alkaloids that modulate the neuronal nicotinic receptor and provide neuroprotection in an Alzheimer's disease model:the case of Teline monspessulana

Despite the advances in combinatorial or synthetic chemis- try and bioinformatics, recent literature has demonstrated the relevance of nature and biomass as a source of new molecules to treat different pathologies, i.e., bioactive com- pounds obtained from Ecteinascidia turbinate to treat some types of cancer or rapamycin from Streptomyces hygroscop- icus to prevent organ rejection after transplant. This trend will continue simply due to the fact that Mother Nature has been synthesizing molecules for millions of years. In our lab- oratory, we have characterized several compounds obtained from natural sources and that possess important neuronal effects,

Response Ability to External Signal Enhanced by Biological Spatial Configuration in Coupled Hindmarsh-Rose Neural System

The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose model. For the proper coupling intensity, we set the control parameter to be near the critical value, and the external stimulus is introduced to the first cell in coupled system. It is found that, on one hand, when the cells are coupled with some proper topological structures, the external stimulus could transmit through the system, and shows better response ability and higher sensitivity. On the other hand, the influence of topological configuration on the synchronous ability and selection effect of neural system are also discussed. Our results display that the topology of coupled system may play an important role in the process of signal propagation, which could help us to understand the coordinated performance of cells in tissue.

Hindmarsh-Rose神经元模型的稳定性与Hopf分支

研究外界刺激参数对Hindmarsh-Rose神经元模型的稳定性与产生Hopf分支的影响。通过导数法、特征值分析及Hurwitz判别准则,得到外界刺激与Hindmarsh-Rose模型平衡点个数变化、平衡点局部稳定性,及该模型在平衡点处经历Hopf分支之间的关系。运用Matlab进行数值仿真,验证了定理的结果,展示了当神经元受到较大外界刺激时出现的复杂现象。

基于Hindmarsh-Rose神经元模型的模式分割

联想记忆和模式分割是大脑的重要功能,大脑海马区是这一功能的重要物质基础。Hindmarsh-Rose神经元模型能够较好地模拟大脑海马区神经元的特性。本文以Hindmarsh-Rose神经元为节点,按Hopfield规则构造网络,同时,考虑到大脑中神经元连接的生理学实际情况,通过数值模拟,实现了在弱、中、强三种连接强度情况下的模式分割以及在随机概率连接情况下的模式分割,通过分析比较,提出了进一步改进的方向。

NeuronSup:基于偏见神经元抑制的深度模型去偏方法

随着深度学习的广泛应用,研究者在关注模型分类性能的同时,还需要关注模型的决策是否公平可信。存在决策偏见的深度模型会造成极大的负面影响,因此如何维持深度模型的分类正确率,同时提高模型的决策公平至关重要。目前已有工作提出了较多方法,用于改善模型的个体公平,但是这些方法仍然在去偏效果、去偏后模型可用性、去偏效率等方面存在缺陷。为此,文中分析了深度模型存在个体偏见时神经元异常激活现象,提出了一种基于偏见神经元抑制的模型去偏方法NeuronSup,具有显著降低个体偏见、对主任务性能影响小、时间复杂度低等优势。具体而言,首先根据深度模型部分神经元由于个体偏见而产生异常激活的现象提出了偏见神经元的概念。然后,利用歧视样本对查找深度模型中的偏见神经元,通过抑制偏见神经元的异常激活大幅降低深度模型的个体偏见,并且根据每个神经元的最大权重边确定主任务性能神经元,通过保持深度模型的主任务性能神经元参数不变,来减小去偏操作对深度模型分类性能造成的影响。因为NeuronSup只对深度模型中的特定神经元进行去偏操作,所以时间复杂度更低,效率更高。最后,在3个真实数据集的6种敏感属性上开展去偏实验,与5种对比算法相比,NeuronSup将个体公平指标THEMIS降低了50%以上,同时使去偏操作对深度模型分类准确率的影响降低到3%以内,验证了NeuronSup在保证深度模型分类能力的情况下降低个体偏见的有效性。