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Generative models for sequential dynamics in active inference. 主动推理中序列动力学的生成模型
IF 3.1 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-12-01 Epub Date: 2023-04-26 DOI: 10.1007/s11571-023-09963-x
Thomas Parr, Karl Friston, Giovanni Pezzulo

A central theme of theoretical neurobiology is that most of our cognitive operations require processing of discrete sequences of items. This processing in turn emerges from continuous neuronal dynamics. Notable examples are sequences of words during linguistic communication or sequences of locations during navigation. In this perspective, we address the problem of sequential brain processing from the perspective of active inference, which inherits from a Helmholtzian view of the predictive (Bayesian) brain. Underneath the active inference lies a generative model; namely, a probabilistic description of how (observable) consequences are generated by (unobservable) causes. We show that one can account for many aspects of sequential brain processing by assuming the brain entails a generative model of the sensed world that comprises central pattern generators, narratives, or well-defined sequences. We provide examples in the domains of motor control (e.g., handwriting), perception (e.g., birdsong recognition) through to planning and understanding (e.g., language). The solutions to these problems include the use of sequences of attracting points to direct complex movements-and the move from continuous representations of auditory speech signals to the discrete words that generate those signals.

理论神经生物学的一个中心主题是,我们的大多数认知操作需要处理离散序列的项目。这种处理反过来又从连续的神经元动力学中产生。著名的例子是语言交流中的单词序列或导航中的位置序列。从这个角度来看,我们从主动推理的角度来解决顺序大脑处理的问题,这继承了Helmholtzian对预测(贝叶斯)大脑的看法。主动推理的背后是生成模型;也就是说,对(可观察的)结果如何由(不可观察的)原因产生的概率描述。我们表明,可以通过假设大脑需要一个由中心模式生成器、叙述或定义良好的序列组成的感知世界的生成模型来解释顺序大脑处理的许多方面。我们提供了从运动控制(例如,手写)、感知(例如,鸟鸣识别)到规划和理解(例如,语言)等领域的例子。这些问题的解决方案包括使用吸引点序列来指导复杂的动作,以及从听觉语音信号的连续表示到生成这些信号的离散单词的移动。
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引用次数: 0
Robust working memory in a two-dimensional continuous attractor network. 二维连续吸引子网络中的鲁棒工作记忆
IF 3.1 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-12-01 Epub Date: 2023-05-29 DOI: 10.1007/s11571-023-09979-3
Weronika Wojtak, Stephen Coombes, Daniele Avitabile, Estela Bicho, Wolfram Erlhagen

Continuous bump attractor networks (CANs) have been widely used in the past to explain the phenomenology of working memory (WM) tasks in which continuous-valued information has to be maintained to guide future behavior. Standard CAN models suffer from two major limitations: the stereotyped shape of the bump attractor does not reflect differences in the representational quality of WM items and the recurrent connections within the network require a biologically unrealistic level of fine tuning. We address both challenges in a two-dimensional (2D) network model formalized by two coupled neural field equations of Amari type. It combines the lateral-inhibition-type connectivity of classical CANs with a locally balanced excitatory and inhibitory feedback loop. We first use a radially symmetric connectivity to analyze the existence, stability and bifurcation structure of 2D bumps representing the conjunctive WM of two input dimensions. To address the quality of WM content, we show in model simulations that the bump amplitude reflects the temporal integration of bottom-up and top-down evidence for a specific combination of input features. This includes the network capacity to transform a stable subthreshold memory trace of a weak input into a high fidelity memory representation by an unspecific cue given retrospectively during WM maintenance. To address the fine-tuning problem, we test numerically different perturbations of the assumed radial symmetry of the connectivity function including random spatial fluctuations in the connection strength. Different to the behavior of standard CAN models, the bump does not drift in representational space but remains stationary at the input position.

连续凹凸吸引子网络(can)在过去被广泛用于解释工作记忆任务的现象学,在工作记忆任务中,连续值信息必须保持以指导未来的行为。标准CAN模型有两个主要的限制:凹凸吸引子的定型形状不能反映WM项目表征质量的差异,网络内的循环连接需要生物学上不现实的微调水平。我们在一个由两个耦合的Amari型神经场方程形式化的二维(2D)网络模型中解决了这两个挑战。它结合了经典can的横向抑制型连接与局部平衡的兴奋和抑制反馈回路。我们首先使用径向对称连通性分析了代表两个输入维的合维WM的二维凸起的存在性、稳定性和分岔结构。为了解决WM内容的质量问题,我们在模型模拟中表明,碰撞幅度反映了输入特征特定组合的自下而上和自上而下证据的时间整合。这包括通过在WM维护期间回溯给出的非特定提示将弱输入的稳定亚阈值记忆痕迹转换为高保真记忆表示的网络能力。为了解决微调问题,我们在数值上测试了假设连接函数径向对称的不同扰动,包括连接强度的随机空间波动。与标准CAN模型的行为不同,凸起不会在表示空间中漂移,而是在输入位置保持静止。
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引用次数: 0
A memristor-based circuit design of avoidance learning with time delay and its application 基于忆阻器的时延回避学习电路设计及其应用
IF 3.7 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-09-19 DOI: 10.1007/s11571-024-10173-2
Junwei Sun, Haojie Wang, Yuanpeng Xu, Peng Liu, Yanfeng Wang

Currently, the research in memristor-based associative memory neural networks pays more attention to positive stimuli and lays less attention to negative stimuli. Negative stimuli are superior to positive stimuli in some ways, but lack the associated circuit implementation. In this paper, a memristor-based circuit design of avoidance learning with time delay is designed. The circuit can respond to a negative stimulus after initial avoidance learning and the effect of delay time between stimuli is considered. The realization of avoidance learning is confirmed in the PSPICE simulation results. In addition, an extended application circuit based on the memristor-based circuit design of avoidance learning with time delay is proposed. The application circuit is based on the advantage of negative stimuli is more difficult to forget than positive stimuli in associative memory. Based on the features of objects as input, the output of the circuit is used to achieve the function of avoidance learning. The application circuit provides more references for neural networks of automatic driving with further development.

目前,基于忆阻器的联想记忆神经网络研究更多地关注正面刺激,而较少关注负面刺激。负刺激在某些方面优于正刺激,但缺乏相关的电路实现。本文设计了一种基于忆阻器的时延回避学习电路。该电路可在初始回避学习后对负刺激做出反应,并考虑了刺激之间延迟时间的影响。PSPICE 仿真结果证实了回避学习的实现。此外,还提出了基于忆阻器电路设计的具有时间延迟的回避学习扩展应用电路。该应用电路基于联想记忆中负面刺激比正面刺激更难遗忘的优势。以对象的特征为输入,利用电路的输出实现回避学习的功能。该应用电路为自动驾驶神经网络的进一步发展提供了更多参考。
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引用次数: 0
Perceptual information processing in table tennis players: based on top-down hierarchical predictive coding 乒乓球运动员的感知信息处理:基于自上而下的分层预测编码
IF 3.7 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-09-13 DOI: 10.1007/s11571-024-10171-4
Ziyi Peng, Lin Xu, Jie Lian, Xin An, Shufang Chen, Yongcong Shao, Fubing Jiao, Jing Lv

Long-term training induces neural plasticity in the visual cognitive processing cortex of table tennis athletes, who perform cognitive processing in a resource-conserving manner. However, further discussion is needed to determine whether the spatial processing advantage of table tennis players manifests in the early stage of sensory input or the late stage of processing. This study aims to explore the processing styles and neural activity characteristics of table tennis players during spatial cognitive processing. Spatial cognitive tasks were completed by 28 college students and 20 s-level table tennis players, and event-related potentials (ERP) data were recorded during the task. The behavioral results showed that the table tennis group performed better on the task than the college students group (control). The ERP results showed that the amplitude of the N1 component of the table tennis group was significantly lower than that of the control group. The amplitude of the P2 and P3 components of the table tennis group was higher than that of the control group. Table tennis players showed significant synergistic activity between electrodes in the β-band. The results of this study suggest that table tennis players significantly deploy attentional resources and cognitive control. Further, they employ stored motor experience to process spatial information in a hierarchical predictive coding manner.

长期训练可诱导乒乓球运动员视觉认知加工皮层的神经可塑性,他们以资源节约型方式进行认知加工。然而,乒乓球运动员的空间加工优势是体现在感觉输入的早期阶段还是加工的晚期阶段,还需要进一步探讨。本研究旨在探讨乒乓球运动员在空间认知加工过程中的加工方式和神经活动特征。28名大学生和20名s级乒乓球运动员完成了空间认知任务,并记录了任务过程中的事件相关电位(ERP)数据。行为结果显示,乒乓球运动员组在任务中的表现优于大学生组(对照组)。ERP结果显示,乒乓球组 N1成分的振幅明显低于对照组。乒乓球组 P2 和 P3 分量的振幅高于对照组。乒乓球运动员在 β 波段的电极间表现出明显的协同活动。本研究的结果表明,乒乓球运动员能显著调配注意力资源和认知控制。此外,他们还利用存储的运动经验,以分层预测编码的方式处理空间信息。
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引用次数: 0
The dynamical behavior effects of different numbers of discrete memristive synaptic coupled neurons 不同数量离散记忆性突触耦合神经元的动态行为效应
IF 3.7 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-09-13 DOI: 10.1007/s11571-024-10172-3
Minyuan Cheng, Kaihua Wang, Xianying Xu, Jun Mou

Two types of neuron models are constructed in this paper, namely the single discrete memristive synaptic neuron model and the dual discrete memristive synaptic neuron model. Firstly, it is proved that both models have only one unstable equilibrium point. Then, the influence of the coupling strength parameters and neural membrane amplification coefficient of the corresponding system of the two models on the rich dynamical behavior of the systems is analyzed. Research has shown that when the number of discrete local active memristor used as simulation synapses in the system increases from one to two, the coupling strength parameter of the same memristor has significantly different effects on the dynamical behavior of the system within the same range, that is, from a state with periodicity, chaos, and periodicity window to a state with only chaos. In addition, under the influence of coupling strength parameters and neural membrane amplification coefficients, the complexity of the system weakens to varying degrees. Moreover, under the effect of two memristors, the system exhibits a rare and interesting phenomenon where the coupling strength parameter and the neural membrane amplification coefficient can mutually serve as control parameter, resulting in the generation of a remerging Feigenbaum tree. Finally, the pseudo-randomness of the chaotic systems corresponding to the two models are detected by NIST SP800-22, and relevant simulation results are verified on the DSP hardware experimental platform. The discrete memristive synaptic neuron models established in this article provide assistance in studying the relevant working principles of real neurons.

本文构建了两种神经元模型,即单离散记忆突触神经元模型和双离散记忆突触神经元模型。首先,证明了这两个模型都只有一个不稳定平衡点。然后,分析了两个模型对应系统的耦合强度参数和神经膜放大系数对系统丰富动力学行为的影响。研究表明,当系统中用作模拟突触的离散局部有源忆阻器的数量从一个增加到两个时,同一忆阻器的耦合强度参数在同一范围内对系统的动力学行为有明显不同的影响,即从具有周期性、混沌性和周期性窗口的状态到只有混沌性的状态。此外,在耦合强度参数和神经膜放大系数的影响下,系统的复杂性也有不同程度的减弱。此外,在两个忆阻器的作用下,系统出现了一种罕见而有趣的现象,即耦合强度参数和神经膜放大系数可以互为控制参数,从而产生一棵重合的费根鲍姆树。最后,通过NIST SP800-22检测了两种模型对应的混沌系统的伪随机性,并在DSP硬件实验平台上验证了相关仿真结果。本文建立的离散记忆突触神经元模型有助于研究真实神经元的相关工作原理。
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引用次数: 0
Advancements in automated diagnosis of autism spectrum disorder through deep learning and resting-state functional mri biomarkers: a systematic review 通过深度学习和静息态功能成像生物标记物自动诊断自闭症谱系障碍的进展:系统综述
IF 3.7 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-09-13 DOI: 10.1007/s11571-024-10176-z
Shiza Huda, Danish Mahmood Khan, Komal Masroor, Warda, Ayesha Rashid, Mariam Shabbir

Autism Spectrum Disorder(ASD) is a type of neurological disorder that is common among children. The diagnosis of this disorder at an early stage is the key to reducing its effects. The major symptoms include anxiety, lack of communication, and less social interaction. This paper presents a systematic review conducted based on PRISMA guidelines for automated diagnosis of ASD. With rapid development in the field of Data Science, numerous methods have been proposed that can diagnose the disease at an early stage which can minimize the effects of the disorder. Machine learning and deep learning have proven suitable techniques for the automated diagnosis of ASD. These models have been developed on various datasets such as ABIDE I and ABIDE II, a frequently used dataset based on rs-fMRI images. Approximately 26 articles have been reviewed after the screening process. The paper highlights a comparison between different algorithms used and their accuracy as well. It was observed that most researchers used DL algorithms to develop the ASD detection model. Different accuracies were recorded with a maximum accuracy close to 0.99. Recommendations for future work have also been discussed in a later section. This analysis derived a conclusion that AI-emerged DL and ML technologies can diagnose ASD through rs-fMRI images with maximum accuracy. The comparative analysis has been included to show the accuracy range.

自闭症谱系障碍(ASD)是一种常见于儿童的神经系统疾病。早期诊断这种疾病是减少其影响的关键。其主要症状包括焦虑、缺乏沟通和社会交往较少。本文介绍了一项基于PRISMA指南对ASD进行自动诊断的系统性综述。随着数据科学领域的快速发展,人们提出了许多能在早期诊断疾病的方法,这些方法能最大限度地减少疾病的影响。机器学习和深度学习已被证明是自动诊断 ASD 的合适技术。这些模型是在 ABIDE I 和 ABIDE II 等各种数据集上开发的,ABIDE I 和 ABIDE II 是基于 rs-fMRI 图像的常用数据集。经过筛选,约有 26 篇文章通过了审核。论文重点比较了所使用的不同算法及其准确性。据观察,大多数研究人员使用 DL 算法来开发 ASD 检测模型。所记录的准确率各不相同,最高准确率接近 0.99。对未来工作的建议也在后面的章节中进行了讨论。本分析得出的结论是,人工智能新兴的 DL 和 ML 技术可以通过 rs-fMRI 图像诊断 ASD,且准确率最高。比较分析显示了准确率的范围。
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引用次数: 0
EEG-based deception detection using weighted dual perspective visibility graph analysis 利用加权双视角可见度图分析进行基于脑电图的欺骗检测
IF 3.7 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-09-13 DOI: 10.1007/s11571-024-10163-4
Ali Rahimi Saryazdi, Farnaz Ghassemi, Zahra Tabanfar, Sheida Ansarinasab, Fahimeh Nazarimehr, Sajad Jafari

Deception detection is a critical aspect across various domains. Integrating advanced signal processing techniques, particularly in neuroscientific studies, has opened new avenues for exploring deception at a deeper level. This study uses electroencephalogram (EEG) signals from a balanced cohort of 22 participants, consisting of both males and females, aged between 22 and 29, engaged in a visual task for instructed deception. We propose a novel approach in the realm of deception detection utilizing the Weighted Dual Perspective Visibility Graph (WDPVG) method to decode instructed deception by converting average epochs from each EEG channel into a complex network. Six graph-based features, including average and deviation of strength, weighted clustering coefficient, weighted clustering coefficient entropy, average weighted shortest path length, and modularity, are extracted, comprehensively representing the underlying brain dynamics associated with deception. Subsequently, these features are employed for classification using three distinct algorithms: K Nearest Neighbors (KNN), Support Vector Machine (SVM), and Decision Tree (DT). Experimental results reveal promising accuracy rates for KNN (66.64%), SVM (86.25%), and DT (82.46%). Furthermore, the features distributions of EEG networks are analyzed across different brain lobes, comparing truth-telling and lying modes. These analyses reveal the frontal and parietal lobes’ potential in distinguishing between truth and deception, highlighting their active role during deceptive behavior. The findings demonstrate the WDPVG method’s effectiveness in decoding deception from EEG signals, offering insights into the neural basis of deceptive behavior. This research could enhance the understanding of neuroscience and deception detection, providing a framework for future real-world applications.

欺骗检测是各个领域的一个重要方面。整合先进的信号处理技术,尤其是神经科学研究中的信号处理技术,为更深层次地探索欺骗开辟了新的途径。本研究使用了 22 名参与者的脑电图(EEG)信号,这些参与者中既有男性也有女性,年龄在 22 岁至 29 岁之间。我们在欺骗检测领域提出了一种新方法,即利用加权双视角可见性图(WDPVG)方法,通过将每个脑电图通道的平均时程转换成一个复杂的网络来解码指示欺骗。该方法提取了六个基于图的特征,包括强度的平均值和偏差、加权聚类系数、加权聚类系数熵、平均加权最短路径长度和模块化程度,全面反映了与欺骗相关的潜在大脑动态。随后,使用三种不同的算法对这些特征进行分类:K 近邻(KNN)、支持向量机(SVM)和决策树(DT)。实验结果表明,KNN(66.64%)、SVM(86.25%)和 DT(82.46%)的准确率很高。此外,还分析了不同脑叶的脑电图网络特征分布,比较了说真话和说谎模式。这些分析揭示了额叶和顶叶在区分真相和欺骗方面的潜力,突出了它们在欺骗行为中的积极作用。研究结果表明,WDPVG 方法能有效地从脑电信号中解码欺骗行为,从而深入了解欺骗行为的神经基础。这项研究可以加深人们对神经科学和欺骗检测的理解,为未来的实际应用提供一个框架。
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引用次数: 0
Regulation of XOR function of reduced human L2/3 pyramidal neurons 调节人体 L2/3 锥体神经元的 XOR 功能
IF 3.7 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-09-12 DOI: 10.1007/s11571-024-10175-0
Yanheng Li, Ruiming Zhang, Xiaojuan Sun

The apical dendrites of human L2/3 pyramidal neurons are capable of performing XOR computation by modulating the amplitude of dendritic calcium action potentials (dCaAPs) mediated by calcium ions. What influences this particular function? There is still no answer to this question. In this study, we employed a rational and feasible reduction method to successfully derive simplified models of human L2/3 pyramidal neurons while preserving their detailed functional properties. Using a conductance-based model, we manipulated the membrane potential of the apical dendrite in the simplified model. Our findings indicate that an increase in sodium conductance (({g}_{Na})) and membrane capacitance (({C}_{m})) weakens the XOR function, while regulation of potassium conductance (({g}_{K})) demonstrates robustness in maintaining the XOR function. Further analysis reveals that when a single pathway is activated, an increase in ({g}_{Na}) and ({C}_{m}) leads to decrease in the amplitude of dCaAPs, whereas increasing ({g}_{K}) has a relatively minor impact on dCaAPs amplitude. In conclusion, although calcium ions play a crucial role in enabling apical dendrites of human L2/3 pyramidal neurons to perform XOR computation, other ion channels’ conductance and membrane capacitance can also influence this function.

人类 L2/3 锥体神经元的顶端树突能够通过调节由钙离子介导的树突钙动作电位(dCaAPs)的振幅来执行 XOR 计算。是什么影响了这一特殊功能?这个问题至今没有答案。在这项研究中,我们采用了一种合理可行的还原方法,在保留人类 L2/3 锥体神经元详细功能特性的同时,成功地推导出了简化模型。利用基于电导的模型,我们操纵了简化模型中顶端树突的膜电位。我们的研究结果表明,钠传导(({g}_{Na}))和膜电容(({C}_{m}))的增加会减弱XOR功能,而钾传导(({g}_{K}))的调节在维持XOR功能方面表现出稳健性。进一步的分析表明,当单一通路被激活时,({g}_{Na})和({C}_{m})的增加会导致dCaAPs振幅的减小,而({g}_{K})的增加对dCaAPs振幅的影响相对较小。总之,尽管钙离子在人类L2/3锥体神经元顶端树突进行XOR计算中起着关键作用,但其他离子通道的电导和膜电容也会影响这一功能。
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引用次数: 0
Fast-slow dynamics in a memristive ion channel-based bionic circuit 基于记忆离子通道的仿生电路中的快慢动力学
IF 3.7 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-09-10 DOI: 10.1007/s11571-024-10168-z
Xincheng Ding, Chengtao Feng, Ning Wang, Ao Liu, Quan Xu

Electrophysiological properties of ion channels can influence the transport process of ions and the generation of firing patterns in an excitable biological neuron when applying an external stimulus and exceeding the excitable threshold. In this paper, a current stimulus is employed to emulate the external stimulus, and a second-order locally active memristor (LAM) is deployed to characterize the properties of ion channels. Then, a simple bionic circuit possessing the LAM, a capacitor, a DC voltage, and the current stimulus is constructed. Fast-slow dynamical effects of the current stimulus with low- and high-frequency are respectively explored. Numerical simulations disclose that the bionic circuit can generate bursting behaviors for the low-frequency current stimulus and spiking behaviors for the high-frequency current stimulus. Besides, fold and Hopf bifurcation sets are deduced and the bifurcation mechanisms for bursting behaviors are elaborated. Furthermore, the numerically simulated bursting and spiking behaviors are verified by PCB-based hardware experiments. These results reflect the feasibility of the bionic circuit in generating the firing patterns of spiking and bursting behaviors and the external current can be employed to regulate these firing patterns.

当施加外部刺激并超过兴奋阈值时,离子通道的电生理特性会影响离子的传输过程以及可兴奋生物神经元的点火模式的产生。本文采用电流刺激来模拟外部刺激,并利用二阶局部有源忆阻器(LAM)来表征离子通道的特性。然后,利用 LAM、电容器、直流电压和电流刺激构建了一个简单的仿生电路。分别探讨了低频和高频电流刺激的快慢动态效应。数值模拟显示,仿生电路在低频电流刺激下能产生突发性行为,在高频电流刺激下能产生尖峰行为。此外,还推导出折叠和霍普夫分岔集,并阐述了猝发行为的分岔机制。此外,基于 PCB 的硬件实验验证了数值模拟的猝发和尖峰行为。这些结果反映了仿生电路在产生尖峰和猝发行为的点火模式方面的可行性,而且外部电流可用于调节这些点火模式。
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引用次数: 0
Investigation on the regular and chaotic dynamics of a ring network of five inertial Hopfield neural network: theoretical, analog and microcontroller simulation 五惯性 Hopfield 神经网络环形网络的规则和混沌动力学研究:理论、模拟和微控制器仿真
IF 3.7 3区 工程技术 Q2 NEUROSCIENCES Pub Date : 2024-09-06 DOI: 10.1007/s11571-024-10170-5
Jean Baptiste Koinfo, Sridevi Sriram, Kengne Jacques, Anitha Karthikeyan

The studies conducted in this contribution are based on the analysis of the dynamics of a homogeneous network of five inertial neurons of the Hopfield type to which a unidirectional ring coupling topology is applied. The coupling is achieved by perturbing the next neuron's amplitude with a signal proportional to the previous one. The system consists of ten coupled ODEs, and the investigations carried out have allowed us to highlight several unusual and rarely related dynamics, hence the importance of emphasizing them. The main analysis tools that have helped in obtaining the results presented are phase portraits, bifurcation diagrams, and the Maximal Lyapunov exponent. In this system, we have observed phenomena such as the coexistence of homogeneous and heterogeneous attractors, period-doubling crisis, parallel branches, and the path leading to hyperchaotic multi-spiral. All attractors are non-hidden as they originate from well-known equilibrium points. The system has 254 equilibrium points, among which only 32 undergo a Hopf bifurcation followed by period-doubling, leading to a merging crisis phenomenon until the final hyperchaotic multi-spiral attractor. For the same parameter values (coupling or dissipation), a maximum of 30 attractors for the coupling coefficient and 32 attractors for dissipation coexist, and illustrated by the phase portraits. Virtual verification using Pspice and practical verification using an Arduino Mega 2580 microcontroller of the model have also been reported. They are in perfect agreement with the behaviors resulting from numerical investigations. The circuit energy and dimensionless energy has been estimated and the scale relation established. The results presented further enrich previous and recent work in the study of the nonlinear dynamics of Hopfield-type neural networks. Additionally, it is important to mention that cyclic coupling typology may be used as an alternative approach in generating multi-spiral signals in Hopfield oscillators.

本文的研究基于对一个由五个 Hopfield 型惯性神经元组成的同质网络的动力学分析,该网络采用了单向环形耦合拓扑结构。耦合是通过用与前一个神经元成比例的信号扰动下一个神经元的振幅来实现的。该系统由十个耦合的 ODE 组成,所进行的研究让我们发现了几个不寻常和罕见的相关动力学,因此强调这些动力学非常重要。有助于获得上述结果的主要分析工具包括相位图、分岔图和最大李雅普诺夫指数。在这个系统中,我们观察到了同质吸引子和异质吸引子共存、周期加倍危机、平行分支以及通向超混沌多螺旋的路径等现象。所有吸引子都是非隐藏的,因为它们都源自众所周知的平衡点。该系统有 254 个平衡点,其中只有 32 个平衡点会发生霍普夫分岔,随后出现周期加倍,导致合并危机现象,直至最终的超混沌多螺旋吸引子。在相同的参数值(耦合或耗散)下,耦合系数最多有 30 个吸引子共存,耗散最多有 32 个吸引子共存,并通过相位图加以说明。此外,还报告了使用 Pspice 对模型进行的虚拟验证,以及使用 Arduino Mega 2580 微控制器对模型进行的实际验证。它们与数值研究的结果完全一致。对电路能量和无量纲能量进行了估算,并建立了比例关系。这些结果进一步丰富了以往和近期对 Hopfield 型神经网络非线性动力学的研究。此外,值得一提的是,循环耦合类型学可用作在 Hopfield 振荡器中产生多螺旋信号的另一种方法。
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引用次数: 0
期刊
Cognitive Neurodynamics
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