Cognitive NeurodynamicsPub Date : 2025-12-01Epub Date: 2025-07-23DOI: 10.1007/s11571-025-10301-6
Ziling Wang, Dandan Qian, Songting Li, Wei Lu, Douglas Zhou
{"title":"Adaptive cholinergic feedback network oscillations: insights into striatal beta oscillations and circuit dynamics.","authors":"Ziling Wang, Dandan Qian, Songting Li, Wei Lu, Douglas Zhou","doi":"10.1007/s11571-025-10301-6","DOIUrl":"10.1007/s11571-025-10301-6","url":null,"abstract":"<p><p>Enhanced beta oscillations (12-25 Hz) within the cortico-basal ganglia-thalamic network are significantly associated with motor deficits and are a prominent characteristic of the neural dynamic pathology in Parkinson's disease. Although the striatum has been proposed as a promising origin for enhanced beta oscillations, the precise mechanism through which distinct striatal neurons collaborate to orchestrate beta oscillations remains elusive. This study constructs a biophysical neural network model of the striatum based on experimental constraints. The model faithfully reproduces various experimental observations, including dopamine-dependent beta oscillations and phase-locked firing patterns. Through both theoretical and numerical analysis, our analysis reveals that striatal beta oscillations emerge from interactions within the cellular architecture, particularly the somatostatin-expressing interneurons (SOM) driven choline acetyltransferase-expressing interneurons (ChAT)-indirect pathway striatal projection neurons (iSPN) loop. Our results underscore the critical role of ChATs in enhancing beta oscillations. ChATs, instead of passively providing excitatory drive, actively amplify beta oscillations by enhancing their excitation efficacy through a phase-locked mode. Additionally, the inhibitory interactions among iSPNs, with robust and slow inhibitory recovery dynamics within iSPNs, potentially result in beta oscillations. The slow inhibitory recovery is likely attributed to the slow dynamics of the KCNQ current. SOMs further modulate the beta oscillations by affecting their downstream ChAT-iSPN loop. These results provide novel insights into the mechanism underlying striatal beta oscillations, shedding light on the processes involved in beta oscillations generation during pathological states.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"117"},"PeriodicalIF":3.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12286910/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144728382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"DSTA-Net: dynamic spatio-temporal feature augmentation network for motor imagery classification.","authors":"Liang Chang, Banghua Yang, Jiayang Zhang, Tie Li, Juntao Feng, Wendong Xu","doi":"10.1007/s11571-025-10296-0","DOIUrl":"10.1007/s11571-025-10296-0","url":null,"abstract":"<p><p>Accurate decoding and strong feature interpretability of Motor Imagery (MI) are expected to drive MI applications in stroke rehabilitation. However, the inherent nonstationarity and high intra-class variability of MI-EEG pose significant challenges in extracting reliable spatio-temporal features. We proposed the Dynamic Spatio-Temporal Feature Augmentation Network (DSTA-Net), which combines DSTA and the Spatio-Temporal Convolution (STC) modules. In DSTA module, multi-scale temporal convolutional kernels tailored to the α and β frequency bands of MI neurophysiological characteristics, while raw EEG serve as a baseline feature layer to retain original information. Next, Grouped Spatial Convolutions extract multi-level spatial features, combined with weight constraints to prevent overfitting. Spatial convolution kernels map EEG channel information into a new spatial domain, enabling further feature extraction through dimensional transformation. And STC module further extracts features and conducts classification. We evaluated DSTA-Net on three public datasets and applied it to a self-collected stroke dataset. In tenfold cross-validation, DSTA-Net achieved average accuracy improvements of 6.29% (<i>p</i> < 0.01), 3.05% (<i>p</i> < 0.01), 5.26% (<i>p</i> < 0.01), and 2.25% over the ShallowConvNet on the BCI-IV-2a, OpenBMI, CASIA, and stroke dataset, respectively. In hold-out validation, DSTA-Net achieved average accuracy improvements of 3.99% (<i>p</i> < 0.01) and 4.2% (<i>p</i> < 0.01) over the ShallowConvNet on the OpenBMI and CASIA datasets, respectively. Finally, we applied DeepLIFT, Common Spatial Pattern, and t-SNE to analyze the contributions of individual EEG channels, extract spatial patterns, and visualize features. The superiority of DSTA-Net offers new insights for further research and application in MI. The code is available in https://github.com/CL-Cloud-BCI/DSTANet-code.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"118"},"PeriodicalIF":3.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12286908/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144728383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cognitive NeurodynamicsPub Date : 2025-12-01Epub Date: 2024-12-31DOI: 10.1007/s11571-024-10185-y
Hui Wang, Xiaxia Xu, Zhuo Yang, Tao Zhang
{"title":"Alterations of synaptic plasticity and brain oscillation are associated with autophagy induced synaptic pruning during adolescence.","authors":"Hui Wang, Xiaxia Xu, Zhuo Yang, Tao Zhang","doi":"10.1007/s11571-024-10185-y","DOIUrl":"10.1007/s11571-024-10185-y","url":null,"abstract":"<p><p>Adolescent brain development is characterized by significant anatomical and physiological alterations, but little is known whether and how these alterations impact the neural network. Here we investigated the development of functional networks by measuring synaptic plasticity and neural synchrony of local filed potentials (LFPs), and further explored the underlying mechanisms. LFPs in the hippocampus were recorded in young (21 ~ 25 days), adolescent (1.5 months) and adult (3 months) rats. Long term potentiation (LTP) and neural synchrony were analyzed. The results showed that the LTP was the lowest in adolescent rats. During development, the theta coupling strength was increased progressively but there was no significant change of gamma coupling between young rats and adolescent rats. The density of dendrite spines was decreased progressively during development. The lowest levels of NR2A, NR2B and PSD95 were detected in adolescent rats. Importantly, it was found that the expression levels of autophagy markers were the highest during adolescent compared to that in other developmental stages. Moreover, there were more co-localization of autophagosome and PSD95 in adolescent rats. It suggests that autophagy is possibly involved in synaptic elimination during adolescence, and further impacts synaptic plasticity and neural synchrony.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"2"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11688264/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cognitive NeurodynamicsPub Date : 2025-12-01Epub Date: 2024-12-31DOI: 10.1007/s11571-024-10182-1
Xudong Zhao, Hualin Wang, Ke Li, Shanguang Chen, Lijuan Hou
{"title":"Beta-band oscillations and spike-local field potential synchronization in the motor cortex are correlated with movement deficits in an exercise-induced fatigue mouse model.","authors":"Xudong Zhao, Hualin Wang, Ke Li, Shanguang Chen, Lijuan Hou","doi":"10.1007/s11571-024-10182-1","DOIUrl":"10.1007/s11571-024-10182-1","url":null,"abstract":"<p><p>Fatigue, a complex and multifaceted symptom, profoundly influences quality of life, particularly among individuals suffering from chronic medical conditions or neurological disorders. This symptom not only exacerbates existing conditions but also hinders daily functioning, thereby perpetuating a vicious cycle of worsening symptoms and reduced physical activity. Given the pivotal role of the motor cortex (M1) in coordinating and executing voluntary movements, understanding how the cortex regulates fatigue is crucial. Despite its importance, the neural mechanisms underlying fatigue remain inadequately explored. In this study, we employed electrophysiological recordings in the M1 region of mice to investigate how excitation-inhibition dynamics and neural oscillations are regulated during exercise-induced fatigue. We observed that fatigue led to decreased voluntary physical activity and cognitive performance, manifesting as reduced running wheel distance, mean speed, exercise intensity, and exploratory behaviour. At the neural level, we detected increased firing frequencies for M1 neurons, including both pyramidal neurons and interneurons, along with heightened beta-band oscillatory activity and stronger coupling between beta-band oscillations and interneurons. These findings enhance our understanding of the mechanisms underlying fatigue, offering insights into behavioural, excitability, and oscillatory changes. The results of this study could pave the way for the development of novel intervention strategies to combat fatigue.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"3"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11688262/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142920741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cognitive NeurodynamicsPub Date : 2025-12-01Epub Date: 2025-01-03DOI: 10.1007/s11571-024-10196-9
Qiang Meng, Lan Tian, Guoyang Liu, Xue Zhang
{"title":"EEG-based cross-subject passive music pitch perception using deep learning models.","authors":"Qiang Meng, Lan Tian, Guoyang Liu, Xue Zhang","doi":"10.1007/s11571-024-10196-9","DOIUrl":"10.1007/s11571-024-10196-9","url":null,"abstract":"<p><p>Pitch plays an essential role in music perception and forms the fundamental component of melodic interpretation. However, objectively detecting and decoding brain responses to musical pitch perception across subjects remains to be explored. In this study, we employed electroencephalography (EEG) as an objective measure to obtain the neural responses of musical pitch perception. The EEG signals from 34 subjects under hearing violin sounds at pitches G3 and B6 were collected with an efficient passive Go/No-Go paradigm. The lightweight modified EEGNet model was proposed for EEG-based pitch classification. Specifically, within-subject modeling with the modified EEGNet model was performed to construct individually optimized models. Subsequently, based on the within-subject model pool, a classifier ensemble (CE) method was adopted to construct the cross-subject model. Additionally, we analyzed the optimal time window of brain decoding for pitch perception in the EEG data and discussed the interpretability of these models. The experiment results show that the modified EEGNet model achieved an average classification accuracy of 77% for within-subject modeling, significantly outperforming other compared methods. Meanwhile, the proposed CE method achieved an average accuracy of 74% for cross-subject modeling, significantly exceeding the chance-level accuracy of 50%. Furthermore, we found that the optimal EEG data window for the pitch perception lies 0.4 to 0.9 s onset. These promising results demonstrate that the proposed methods can be effectively used in the objective assessment of pitch perception and have generalization ability in cross-subject modeling.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"6"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11699146/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142930820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cognitive NeurodynamicsPub Date : 2025-12-01Epub Date: 2025-01-09DOI: 10.1007/s11571-024-10184-z
Qiang Li
{"title":"Visual image reconstructed without semantics from human brain activity using linear image decoders and nonlinear noise suppression.","authors":"Qiang Li","doi":"10.1007/s11571-024-10184-z","DOIUrl":"10.1007/s11571-024-10184-z","url":null,"abstract":"<p><p>In recent years, substantial strides have been made in the field of visual image reconstruction, particularly in its capacity to generate high-quality visual representations from human brain activity while considering semantic information. This advancement not only enables the recreation of visual content but also provides valuable insights into the intricate processes occurring within high-order functional brain regions, contributing to a deeper understanding of brain function. However, considering fusion semantics in reconstructing visual images from brain activity involves semantic-to-image guide reconstruction and may ignore underlying neural computational mechanisms, which does not represent true reconstruction from brain activity. In response to this limitation, our study introduces a novel approach that combines linear mapping with nonlinear noise suppression to reconstruct visual images perceived by subjects based on their brain activity patterns. The primary challenge associated with linear mapping lies in its susceptibility to noise interference. To address this issue, we leverage a flexible denoised deep convolutional neural network, which can suppress noise from linear mapping. Our investigation encompasses linear mapping as well as the training of shallow and deep autoencoder denoised neural networks, including a pre-trained, state-of-the-art denoised neural network. The outcome of our study reveals that combining linear image decoding with nonlinear noise reduction significantly enhances the quality of reconstructed images from human brain activity. This suggests that our methodology holds promise for decoding intricate perceptual experiences directly from brain activity patterns without semantic information. Moreover, the model has strong neural explanatory power because it shares structural and functional similarities with the visual brain.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"20"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11718044/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142969971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sg-snn: a self-organizing spiking neural network based on temporal information.","authors":"Shouwei Gao, Ruixin Zhu, Yu Qin, Wenyu Tang, Hao Zhou","doi":"10.1007/s11571-024-10199-6","DOIUrl":"10.1007/s11571-024-10199-6","url":null,"abstract":"<p><p>Neurodynamic observations indicate that the cerebral cortex evolved by self-organizing into functional networks, These networks, or distributed clusters of regions, display various degrees of attention maps based on input. Traditionally, the study of network self-organization relies predominantly on static data, overlooking temporal information in dynamic neuromorphic data. This paper proposes Temporal Self-Organizing (TSO) method for neuromorphic data processing using a spiking neural network. The TSO method incorporates information from multiple time steps into the selection strategy of the Best Matching Unit (BMU) neurons. It enables the coupled BMUs to radiate the weight across the same layer of neurons, ultimately forming a hierarchical self-organizing topographic map of concern. Additionally, we simulate real neuronal dynamics, introduce a glial cell-mediated Glial-LIF (Leaky Integrate-and-fire) model, and adjust multiple levels of BMUs to optimize the attention topological map.Experiments demonstrate that the proposed Self-organizing Glial Spiking Neural Network (SG-SNN) can generate attention topographies for dynamic event data from coarse to fine. A heuristic method based on cognitive science effectively guides the network's distribution of excitatory regions. Furthermore, the SG-SNN shows improved accuracy on three standard neuromorphic datasets: DVS128-Gesture, CIFAR10-DVS, and N-Caltech 101, with accuracy improvements of 0.3%, 2.4%, and 0.54% respectively. Notably, the recognition accuracy on the DVS128-Gesture dataset reaches 99.3%, achieving state-of-the-art (SOTA) performance.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"14"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11718035/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142969959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cognitive NeurodynamicsPub Date : 2025-12-01Epub Date: 2025-01-13DOI: 10.1007/s11571-024-10212-y
Rituparna Bhattacharyya, Brajesh Kumar Jha
{"title":"A fuzzy based computational model to analyze the influence of mitochondria, buffer, and ER fluxes on cytosolic calcium distribution in neuron cells.","authors":"Rituparna Bhattacharyya, Brajesh Kumar Jha","doi":"10.1007/s11571-024-10212-y","DOIUrl":"10.1007/s11571-024-10212-y","url":null,"abstract":"<p><p>A free calcium ion in the cytosol is essential for many physiological and physical functions. Also, it is known as a second messenger as the quantity of free calcium ions is an essential part of brain signaling. In this work, we have attempted to study calcium signaling in the presence of mitochondria, buffer, and endoplasmic reticulum fluxes. Small organelles called mitochondria are found in the nervous system and are involved in several cellular functions, including energy production, response to stress, calcium homeostasis regulation, and pathways leading to cell death. It has been discovered that buffer, endoplasmic reticulum, and mitochondria significantly affect calcium signaling. To investigate how various circumstances impact the quantity of calcium in the cytosol, a mathematical model of a second-order linear partial differential equation with fuzzy boundary conditions has been developed. Systems having ambiguous or imprecise boundary values can be effectively modeled and simulated with the help of fuzzy boundary conditions. Models can provide more dependable and instructive outcomes and become adaptable to real-world circumstances by implementing fuzzy logic into boundary conditions. In this paper, we observed the Fuzzy Laplace Transform to solve variable coefficient fuzzy differential equations using triangular fuzzy numbers. It is noted that maintaining the delicate calcium ion balance, which controls essential cellular functions, depends on the buffer affinity. Also, neurodegenerative illnesses like Alzheimer's, Parkinson's, etc. are linked to disruptions in the control of components such as buffers, mitochondria, and the endoplasmic reticulum.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"25"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11729615/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143001552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The potential associations between acupuncture sensation and brain functional network: a EEG study.","authors":"Dongyang Shen, Banghua Yang, Jing Li, Jiayang Zhang, Yongcong Li, Guofu Zhang, Yanyan Zheng","doi":"10.1007/s11571-025-10233-1","DOIUrl":"10.1007/s11571-025-10233-1","url":null,"abstract":"<p><p>Acupuncture has been widely used as an effective treatment for post-stroke rehabilitation. However, the potential association between acupuncture sensation, an important factor influencing treatment efficacy, and brain functional network is unclear. This research sought to reveal and quantify the changes in brain functional network associated with acupuncture sensation. So multi-channel EEG signals were collected from 30 healthy participants and the Massachusetts General Hospital Acupuncture Sensation Scale (MASS) was utilized to assess their needling sensations. Phase Lag Index (PLI) was used to construct the brain functional network, which was analyzed with graph theoretic methods. It showed that in the needle insertion (NI) state the MASS Index was significantly higher than in the needle retention (NR) state (<i>P</i> < 0.001), and the mean values of PLI were also higher than in the Pre-Rest state and NR state significantly (<i>P</i> < 0.01). In the NI state global efficiency, local efficiency, nodal efficiency, and degree centrality were significantly higher than in the Pre-Rest state and the NR state (<i>P</i> < 0.05), while the opposite is true for the shortest path length (<i>P</i> < 0.01). Then Pearson correlation analysis showed a correlation between MASS Index and graph theory metrics (<i>P</i> < 0.05). Finally, Support Vector Regression (SVR) was used to predict the MASS Index with a minimum mean absolute error of 0.65. These findings suggest that the NI state of acupuncture treatment changes the structure of the brain functional network and affects the graph theory metrics of the brain functional network, which may be an objective biomarker for quantitative evaluation of acupuncture sensation.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s11571-025-10233-1.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"49"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11910458/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143647571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cognitive NeurodynamicsPub Date : 2025-12-01Epub Date: 2025-04-19DOI: 10.1007/s11571-025-10241-1
Fanghai Zhang, Changlin Zhan
{"title":"Multiple generalized stability of nonlinear delayed systems subject to impulsive disturbance.","authors":"Fanghai Zhang, Changlin Zhan","doi":"10.1007/s11571-025-10241-1","DOIUrl":"10.1007/s11571-025-10241-1","url":null,"abstract":"<p><p>The multiple generalized stability of nonlinear systems with impulsive disturbance and distributed delays is studied in this paper. By using the state space partition method, the number of multiple equilibrium points for <i>n</i>-dimensional system is given by <math> <mrow><msubsup><mo>∏</mo> <mrow><mi>i</mi> <mo>=</mo> <mn>1</mn></mrow> <mi>n</mi></msubsup> <mrow><mo>(</mo> <mn>2</mn> <msub><mi>K</mi> <mi>i</mi></msub> <mo>+</mo> <mn>1</mn> <mo>)</mo></mrow> </mrow> </math> with integer <math> <mrow><msub><mi>K</mi> <mi>i</mi></msub> <mo>≥</mo> <mn>0</mn></mrow> </math> , and the sufficient conditions for generalized stability of <math> <mrow><msubsup><mo>∏</mo> <mrow><mi>i</mi> <mo>=</mo> <mn>1</mn></mrow> <mi>n</mi></msubsup> <mrow><mo>(</mo> <msub><mi>K</mi> <mi>i</mi></msub> <mo>+</mo> <mn>1</mn> <mo>)</mo></mrow> </mrow> </math> equilibrium points are derived. Finally, the theoretical results are illustrated by using the simulations of an example.</p>","PeriodicalId":10500,"journal":{"name":"Cognitive Neurodynamics","volume":"19 1","pages":"64"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12009267/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143961756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}