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Gao L, Wu H, Cheng W, Lan B, Ren H, Zhang L, Wang L. Enhanced Descending Corticomuscular Coupling During Hand Grip With Static Force Compared With Enhancing Force. Clin EEG Neurosci 2021; 52:436-443. [PMID: 32611201 DOI: 10.1177/1550059420933149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The interaction between cortex and muscles under hand motor with different force states has not been quantitatively investigated yet, which to some extent places the optimized movement tasks design for brain-computer interface (BCI) applications in hand motor rehabilitation under uncertainty. Converging evidence has suggested that both the descending corticospinal pathway and ascending sensory feedback pathway are involved in the generation of corticomuscular coupling. The present study aimed to explore the corticomuscular coupling during hand motor task with enhancing force and steady-state force. Twenty healthy subjects performed precision grip with enhancing and static force using the right hand with visual feedback of exerted force. Mutual information and Granger causal connectivity were assessed between electroencephalography (EEG) over primary motor cortex and electromyography (EMG) recordings, and statistically analyzed. The results showed that the mutual information value was significantly larger for static force in the beta and alpha frequency band than enhancing force state. Furthermore, compared with enhancing force, the Granger causal connectivity of descending pathways from cortex to muscle was significantly larger for static force in the beta and high alpha frequency band (10-20 Hz), indicating the connection between the primary motor cortex and muscle was strengthened for static force. In summary, the hand grip with static force resulted in an increasing corticomuscular coupling from EEG over the primary motor cortex to EMG compared with enhancing force, implying more attention was required in the static force state. These results have important implications toward motor rehabilitation therapy design for the recovery of impaired hand motor functions.
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Affiliation(s)
- Lin Gao
- State Key Laboratory of Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China.,School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China.,Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi'an University of Technology, Xi'an, Shaanxi, People's Republic of China
| | - Hongjian Wu
- Key Laboratory of Biomedical Information Engineering of Education Ministry, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China.,National Engineering Research Center of Health Care and Medical Devices Xi'an Jiaotong University Branch, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China
| | - Wei Cheng
- State Key Laboratory of Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China.,School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China
| | - Beidi Lan
- Department of Structural Heart Disease, The First Affiliated Hospital of Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China
| | - Haipeng Ren
- Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi'an University of Technology, Xi'an, Shaanxi, People's Republic of China
| | - Lu Zhang
- State Key Laboratory of Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China.,School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China
| | - Ling Wang
- State Key Laboratory of Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China.,School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China
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2
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Barrio R, Ibáñez S, Pérez L, Serrano S. Classification of fold/hom and fold/Hopf spike-adding phenomena. CHAOS (WOODBURY, N.Y.) 2021; 31:043120. [PMID: 34251261 DOI: 10.1063/5.0037942] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Accepted: 03/26/2021] [Indexed: 06/13/2023]
Abstract
The Hindmarsh-Rose neural model is widely accepted as an important prototype for fold/hom and fold/Hopf burstings. In this paper, we are interested in the mechanisms for the production of extra spikes in a burst, and we show the whole parametric panorama in an unified way. In the fold/hom case, two types are distinguished: a continuous one, where the bursting periodic orbit goes through bifurcations but persists along the whole process and a discontinuous one, where the transition is abrupt and happens after a sequence of chaotic events. In the former case, we speak about canard-induced spike-adding and in the second one, about chaos-induced spike-adding. For fold/Hopf bursting, a single (and continuous) mechanism is distinguished. Separately, all these mechanisms are presented, to some extent, in the literature. However, our full perspective allows us to construct a spike-adding map and, more significantly, to understand the dynamics exhibited when borders are crossed, that is, transitions between types of processes, a crucial point not previously studied.
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Affiliation(s)
- Roberto Barrio
- Departamento de Matemática Aplicada and IUMA, Computational Dynamics Group, University of Zaragoza, Zaragoza E-50009, Spain
| | - Santiago Ibáñez
- Departamento de Matemáticas, University of Oviedo, E-33007 Oviedo, Spain
| | - Lucía Pérez
- Departamento de Matemáticas, University of Oviedo, E-33007 Oviedo, Spain
| | - Sergio Serrano
- Departamento de Matemática Aplicada and IUMA, Computational Dynamics Group, University of Zaragoza, Zaragoza E-50009, Spain
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3
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Fatoyinbo HO, Brown RG, Simpson DJW, van Brunt B. Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells. Bull Math Biol 2020; 82:95. [PMID: 32676881 DOI: 10.1007/s11538-020-00771-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 06/26/2020] [Indexed: 11/26/2022]
Abstract
Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of [Formula: see text] and [Formula: see text] fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris-Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris-Lecar model concentrate on external applied current, whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.
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Affiliation(s)
- H O Fatoyinbo
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand.
| | - R G Brown
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand
| | - D J W Simpson
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand
| | - B van Brunt
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand
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4
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Follmann R, Shaffer A, Mobille Z, Rutherford G, Rosa E. Synchronous tonic-to-bursting transitions in a neuronal hub motif. CHAOS (WOODBURY, N.Y.) 2018; 28:106315. [PMID: 30384663 DOI: 10.1063/1.5039880] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2018] [Accepted: 08/17/2018] [Indexed: 06/08/2023]
Abstract
We study a heterogeneous neuronal network motif where a central node (hub neuron) is connected via electrical synapses to other nodes (peripheral neurons). Our numerical simulations show that the networked neurons synchronize in three different states: (i) robust tonic, (ii) robust bursting, and (iii) tonic initially evolving to bursting through a period-doubling cascade and chaos transition. This third case displays interesting features, including the carrying on of a characteristic firing rate found in the single neuron tonic-to-bursting transition.
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Affiliation(s)
- Rosangela Follmann
- School of Information Technology, Illinois State University, Normal, Illinois 61790, USA
| | - Annabelle Shaffer
- Department of Physics, Illinois State University, Normal, Illinois 61790, USA
| | - Zachary Mobille
- Department of Physics, Illinois State University, Normal, Illinois 61790, USA
| | - George Rutherford
- Department of Physics, Illinois State University, Normal, Illinois 61790, USA
| | - Epaminondas Rosa
- Department of Physics, Illinois State University, Normal, Illinois 61790, USA
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5
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Nazarimehr F, Jafari S, Hashemi Golpayegani SMR, Perc M, Sprott JC. Predicting tipping points of dynamical systems during a period-doubling route to chaos. CHAOS (WOODBURY, N.Y.) 2018; 28:073102. [PMID: 30070493 DOI: 10.1063/1.5038801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2018] [Accepted: 06/26/2018] [Indexed: 05/21/2023]
Abstract
Classical indicators of tipping points have limitations when they are applied to an ecological and a biological model. For example, they cannot correctly predict tipping points during a period-doubling route to chaos. To counter this limitation, we here try to modify four well-known indicators of tipping points, namely the autocorrelation function, the variance, the kurtosis, and the skewness. In particular, our proposed modification has two steps. First, the dynamic of the considered system is estimated using its time-series. Second, the original time-series is divided into some sub-time-series. In other words, we separate the time-series into different period-components. Then, the four different tipping point indicators are applied to the extracted sub-time-series. We test our approach on an ecological model that describes the logistic growth of populations and on an attention-deficit-disorder model. Both models show different tipping points in a period-doubling route to chaos, and our approach yields excellent results in predicting these tipping points.
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Affiliation(s)
- Fahimeh Nazarimehr
- Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
| | - Sajad Jafari
- Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
| | | | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, Maribor SI-2000, Slovenia
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Routes to Chaos Induced by a Discontinuous Resetting Process in a Hybrid Spiking Neuron Model. Sci Rep 2018; 8:379. [PMID: 29321626 PMCID: PMC5762689 DOI: 10.1038/s41598-017-18783-z] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Accepted: 12/18/2017] [Indexed: 11/09/2022] Open
Abstract
Several hybrid spiking neuron models combining continuous spike generation mechanisms and discontinuous resetting processes following spiking have been proposed. The Izhikevich neuron model, for example, can reproduce many spiking patterns. This model clearly possesses various types of bifurcations and routes to chaos under the effect of a state-dependent jump in the resetting process. In this study, we focus further on the relation between chaotic behaviour and the state-dependent jump, approaching the subject by comparing spiking neuron model versions with and without the resetting process. We first adopt a continuous two-dimensional spiking neuron model in which the orbit in the spiking state does not exhibit divergent behaviour. We then insert the resetting process into the model. An evaluation using the Lyapunov exponent with a saltation matrix and a characteristic multiplier of the Poincar'e map reveals that two types of chaotic behaviour (i.e. bursting chaotic spikes and near-period-two chaotic spikes) are induced by the resetting process. In addition, we confirm that this chaotic bursting state is generated from the periodic spiking state because of the slow- and fast-scale dynamics that arise when jumping to the hyperpolarization and depolarization regions, respectively.
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Jia Y, Gu H, Luo Q. Sample entropy reveals an age-related reduction in the complexity of dynamic brain. Sci Rep 2017; 7:7990. [PMID: 28801672 PMCID: PMC5554148 DOI: 10.1038/s41598-017-08565-y] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2017] [Accepted: 07/13/2017] [Indexed: 12/16/2022] Open
Abstract
Dynamic reconfiguration of the human brain is characterized by the nature of complexity. The purpose of this study was to measure such complexity and also analyze its association with age. We modeled the dynamic reconfiguration process by dynamic functional connectivity, which was established by resting-state functional magnetic resonance imaging (fMRI) data, and we measured complexity within the dynamic functional connectivity by sample entropy (SampEn). A brainwide map of SampEn in healthy subjects shows larger values in the caudate, the olfactory gyrus, the amygdala, and the hippocampus, and lower values in primary sensorimotor and visual areas. Association analysis in healthy subjects indicated that SampEn of the amygdala-cortical connectivity decreases with advancing age. Such age-related loss of SampEn, however, disappears in patients with schizophrenia. These findings suggest that SampEn of the dynamic functional connectivity is a promising indicator of normal aging.
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Affiliation(s)
- Yanbing Jia
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, P. R. China
| | - Huaguang Gu
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, P. R. China.
| | - Qiang Luo
- School of Life Sciences, Fudan University, Shanghai, 200433, P. R. China. .,Institute of Science and Technology of Brain-Inspired Intelligence, Fudan University, Shanghai, 200433, P. R. China.
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8
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Zhao Z, Gu H. Transitions between classes of neuronal excitability and bifurcations induced by autapse. Sci Rep 2017; 7:6760. [PMID: 28755006 PMCID: PMC5533805 DOI: 10.1038/s41598-017-07051-9] [Citation(s) in RCA: 57] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Accepted: 06/21/2017] [Indexed: 11/10/2022] Open
Abstract
Neuronal excitabilities behave as the basic and important dynamics related to the transitions between firing and resting states, and are characterized by distinct bifurcation types and spiking frequency responses. Switches between class I and II excitabilities induced by modulations outside the neuron (for example, modulation to M-type potassium current) have been one of the most concerning issues in both electrophysiology and nonlinear dynamics. In the present paper, we identified switches between 2 classes of excitability and firing frequency responses when an autapse, which widely exists in real nervous systems and plays important roles via self-feedback, is introduced into the Morris-Lecar (ML) model neuron. The transition from class I to class II excitability and from class II to class I spiking frequency responses were respectively induced by the inhibitory and excitatory autapse, which are characterized by changes of bifurcations, frequency responses, steady-state current-potential curves, and nullclines. Furthermore, we identified codimension-1 and -2 bifurcations and the characteristics of the current-potential curve that determine the transitions. Our results presented a comprehensive relationship between 2 classes of neuronal excitability/spiking characterized by different types of bifurcations, along with a novel possible function of autapse or self-feedback control on modulating neuronal excitability.
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Affiliation(s)
- Zhiguo Zhao
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China
| | - Huaguang Gu
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China.
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9
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Jia B, Gu H, Xue L. A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space. Cogn Neurodyn 2017; 11:189-200. [PMID: 28348650 DOI: 10.1007/s11571-017-9422-8] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2016] [Revised: 12/22/2016] [Accepted: 01/24/2017] [Indexed: 10/20/2022] Open
Abstract
Two different bifurcation scenarios of firing patterns with decreasing extracellular calcium concentrations were observed in identical sciatic nerve fibers of a chronic constriction injury (CCI) model when the extracellular 4-aminopyridine concentrations were fixed at two different levels. Both processes proceeded from period-1 bursting to period-1 spiking via complex or simple processes. Multiple typical experimental examples manifested dynamics closely matching those simulated in a recently proposed 4-dimensional model to describe the nonlinear dynamics of the CCI model, which included most cases of the bifurcation scenarios. As the extracellular 4-aminopyridine concentrations is increased, the structure of the bifurcation scenario becomes more complex. The results provide a basic framework for identifying the relationships between different neural firing patterns and different bifurcation scenarios and for revealing the complex nonlinear dynamics of neural firing patterns. The potential roles of the basic bifurcation structures in identifying the information process mechanism are discussed.
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Affiliation(s)
- Bing Jia
- State Key Laboratory of Medical Neurobiology, Department of Physiology and Biophysics, School of Life Sciences and Collaborative Innovation Centre for Brain Science, Fudan University, Shanghai, 200438 People's Republic of China
| | - Huaguang Gu
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092 People's Republic of China
| | - Lei Xue
- State Key Laboratory of Medical Neurobiology, Department of Physiology and Biophysics, School of Life Sciences and Collaborative Innovation Centre for Brain Science, Fudan University, Shanghai, 200438 People's Republic of China
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10
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Chaos and Hyperchaos in a Model of Ribosome Autocatalytic Synthesis. Sci Rep 2016; 6:38870. [PMID: 27941909 PMCID: PMC5151018 DOI: 10.1038/srep38870] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2016] [Accepted: 11/14/2016] [Indexed: 02/07/2023] Open
Abstract
Any vital activities of the cell are based on the ribosomes, which not only provide the basic machinery for the synthesis of all proteins necessary for cell functioning during growth and division, but for biogenesis itself. From this point of view, ribosomes are self-replicating and autocatalytic structures. In current work we present an elementary model in which the autocatalytic synthesis of ribosomal RNA and proteins, as well as enzymes ensuring their degradation are described with two monotonically increasing functions. For certain parameter values, the model, consisting of one differential equation with delayed argument, demonstrates both stationary and oscillatory dynamics of the ribosomal protein synthesis, which can be chaotic and hyperchaotic dependent on the value of the delayed argument. The biological interpretation of the modeling results and parameter estimation suggest the feasibility of chaotic dynamics in molecular genetic systems of eukaryotes, which depends only on the internal characteristics of functioning of the translation system.
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11
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Khlebodarova TM, Kogai VV, Fadeev SI, Likhoshvai VA. Chaos and hyperchaos in simple gene network with negative feedback and time delays. J Bioinform Comput Biol 2016; 15:1650042. [PMID: 28052708 DOI: 10.1142/s0219720016500426] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Today there are examples that prove the existence of chaotic dynamics at all levels of organization of living systems, except intracellular, although such a possibility has been theoretically predicted. The lack of experimental evidence of chaos generation at the intracellular level in vivo may indicate that during evolution the cell got rid of chaos. This work allows the hypothesis that one of the possible mechanisms for avoiding chaos in gene networks can be a negative evolutionary selection, which prevents fixation or realization of regulatory circuits, creating too mild, from the biological point of view, conditions for the emergence of chaos. It has been shown that one of such circuits may be a combination of negative autoregulation of expression of transcription factors at the level of their synthesis and degradation. The presence of such a circuit results in formation of multiple branches of chaotic solutions as well as formation of hyperchaos with equal and sufficiently low values of the delayed argument that can be implemented not only in eukaryotic, but in prokaryotic cells.
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Affiliation(s)
- Tamara M Khlebodarova
- * Institute of Cytology and Genetics, Siberian Branch, Russian Academy of Sciences, pr., Lavrentieva 10, Novosibirsk, 630090, Russia
| | - Vladislav V Kogai
- † Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Prospect Koptyuga 4, Novosibirsk, 630090, Russia
| | - Stanislav I Fadeev
- † Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Prospect Koptyuga 4, Novosibirsk, 630090, Russia
| | - Vitaly A Likhoshvai
- * Institute of Cytology and Genetics, Siberian Branch, Russian Academy of Sciences, pr., Lavrentieva 10, Novosibirsk, 630090, Russia.,‡ Novosibirsk State University, av. Pirogova 2, Novosibirsk, 630090, Russia
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12
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Xu Y, Wang C, Lv M, Tang J. Local pacing, noise induced ordered wave in a 2D lattice of neurons. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.05.030] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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13
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Huaguang G, Zhiguo Z, Bing J, Shenggen C. Dynamics of on-off neural firing patterns and stochastic effects near a sub-critical Hopf bifurcation. PLoS One 2015; 10:e0121028. [PMID: 25867027 PMCID: PMC4395087 DOI: 10.1371/journal.pone.0121028] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2014] [Accepted: 02/07/2015] [Indexed: 11/18/2022] Open
Abstract
On-off firing patterns, in which repetition of clusters of spikes are interspersed with epochs of subthreshold oscillations or quiescent states, have been observed in various nervous systems, but the dynamics of this event remain unclear. Here, we report that on-off firing patterns observed in three experimental models (rat sciatic nerve subject to chronic constrictive injury, rat CA1 pyramidal neuron, and rabbit blood pressure baroreceptor) appeared as an alternation between quiescent state and burst containing multiple period-1 spikes over time. Burst and quiescent state had various durations. The interspike interval (ISI) series of on-off firing pattern was suggested as stochastic using nonlinear prediction and autocorrelation function. The resting state was changed to a period-1 firing pattern via on-off firing pattern as the potassium concentration, static pressure, or depolarization current was changed. During the changing process, the burst duration of on-off firing pattern increased and the duration of the quiescent state decreased. Bistability of a limit cycle corresponding to period-1 firing and a focus corresponding to resting state was simulated near a sub-critical Hopf bifurcation point in the deterministic Morris-Lecar (ML) model. In the stochastic ML model, noise-induced transitions between the coexisting regimes formed an on-off firing pattern, which closely matched that observed in the experiment. In addition, noise-induced exponential change in the escape rate from the focus, and noise-induced coherence resonance were identified. The distinctions between the on-off firing pattern and stochastic firing patterns generated near three other types of bifurcations of equilibrium points, as well as other viewpoints on the dynamics of on-off firing pattern, are discussed. The results not only identify the on-off firing pattern as noise-induced stochastic firing pattern near a sub-critical Hopf bifurcation point, but also offer practical indicators to discriminate bifurcation types and neural excitability types.
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Affiliation(s)
- Gu Huaguang
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
- * E-mail:
| | - Zhao Zhiguo
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
| | - Jia Bing
- Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China
| | - Chen Shenggen
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
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14
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Minati L. Experimental dynamical characterization of five autonomous chaotic oscillators with tunable series resistance. CHAOS (WOODBURY, N.Y.) 2014; 24:033110. [PMID: 25273190 DOI: 10.1063/1.4890530] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
In this paper, an experimental characterization of the dynamical properties of five autonomous chaotic oscillators, based on bipolar-junction transistors and obtained de-novo through a genetic algorithm in a previous study, is presented. In these circuits, a variable resistor connected in series to the DC voltage source acts as control parameter, for a range of which the largest Lyapunov exponent, correlation dimension, approximate entropy, and amplitude variance asymmetry are calculated, alongside bifurcation diagrams and spectrograms. Numerical simulations are compared to experimental measurements. The oscillators can generate a considerable variety of regular and chaotic sine-like and spike-like signals.
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Affiliation(s)
- Ludovico Minati
- MR-Lab, Center for Mind/Brain Science, University of Trento, Trento, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan, Italy
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