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Wu Y, Sun Z. Detecting stochastic multiresonance in neural networks via statistical complexity measure. Sci Rep 2024; 14:5276. [PMID: 38438571 PMCID: PMC10912744 DOI: 10.1038/s41598-024-55997-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 02/29/2024] [Indexed: 03/06/2024] Open
Abstract
This paper employs statistical complexity measure (SCM) to investigate the occurrence of stochastic multiresonance (SMR) induced by noise and time delay in small-world neural networks coupled with FitzHugh-Nagumo (FHN) neurons. Our findings reveal that SCM exhibits four local maxima at four optimal noise levels, providing evidence for the occurrence of quadruple stochastic resonances. When time delay τ is taken into account in the information transmission, under moderate noise levels, SCM shows several local maxima when τ = n T e with n being a positive integer and T e being the period of subthreshold signal. This indicates the appearance of delay-induced SMR at the multiples of the period of subthreshold signal. Intriguingly, at low noise levels, a strong coherence between time delay and neuronal firing dynamics emerges at τ = n T e - 2 , as confirmed by a series of SCM maxima at these time delays. Furthermore, the study demonstrates that by adjusting the degrees and sizes of small-world networks, as well as the coupling strength, it is possible to optimize the strength of delay-induced SMR, thus maximizing the detection capability of subthreshold signal. The research results may provide us with an effective approach for understanding the role of time delay in signal detection and information transmission.
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Affiliation(s)
- Yazhen Wu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, China
- Maths and Information Technology School, Yuncheng University, Yuncheng, 044000, China
| | - Zhongkui Sun
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, China.
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Jia Y, Gu H, Li Y. Influence of inhibitory autapses on synchronization of inhibitory network gamma oscillations. Cogn Neurodyn 2023; 17:1131-1152. [PMID: 37786650 PMCID: PMC10542088 DOI: 10.1007/s11571-022-09856-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Revised: 06/22/2022] [Accepted: 07/12/2022] [Indexed: 11/30/2022] Open
Abstract
A recent experimental study showed that inhibitory autapses favor firing synchronization of parvalbumin interneurons in the neocortex during gamma oscillations. In the present paper, to provide a comprehensive and deep understanding to the experimental observation, the influence of inhibitory autapses on synchronization of interneuronal network gamma oscillations is theoretically investigated. Weak, middle, and strong synchronizations of a globally inhibitory coupled network composed of Wang-Buzsáki model without autapses appear at the bottom-left, middle, and top-right of the parameter plane with the conductance (gsyn) and the decay constant (τsyn) of inhibitory synapses taken as the x-axis and y-axis, respectively. After introducing inhibitory autapses, the border between the strong and middle synchronizations in the (gsyn, τsyn) plane moves to the top-right with increasing the conductance (gaut) and the decay constant (τaut) of autapses, due to that interspike interval of the single neuron becomes longer, leading to that larger τsyn is needed to ensure the strong synchronization. Then, the synchronization degree of middle and strong synchronizations around the border in the (gsyn, τsyn) plane decreases, while of strong synchronization in the remaining region remains unchanged. The synchronization degree of weak synchronization increases with increasing τaut and gaut, due to that the inhibitory autaptic current becomes strong and long to facilitate synchronization. The enhancement of weak synchronization modulated by inhibitory autapses is also simulated in the random, small-world, and scale-free networks, which may provide explanations to the experimental observation. These results present complex dynamics of synchronization modulated by inhibitory autapses, which needs future experimental demonstrations.
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Affiliation(s)
- Yanbing Jia
- School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471000 China
| | - Huaguang Gu
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092 China
| | - Yuye Li
- College of Mathematics and Computer Science, Chifeng University, Chifeng, 024000 China
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Qi C, Li Y, Gu H, Yang Y. Nonlinear mechanism for the enhanced bursting activities induced by fast inhibitory autapse and reduced activities by fast excitatory autapse. Cogn Neurodyn 2023; 17:1093-1113. [PMID: 37522049 PMCID: PMC10374520 DOI: 10.1007/s11571-022-09872-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2021] [Revised: 07/28/2022] [Accepted: 08/13/2022] [Indexed: 08/01/2023] Open
Abstract
The paradoxical phenomena that excitatory modulation does not enhance but reduces or inhibitory modulation not suppresses but promotes neural firing activities have attracted increasing attention. In the present study, paradoxical phenomena induced by both fast excitatory and inhibitory autapses in a "Fold/Big Homoclinic" bursting are simulated, and the corresponding nonlinear and biophysical mechanisms are presented. Firstly, the enhanced conductance of excitatory autapse induces the number of spikes per burst and firing rate reduced, while the enhanced inhibitory autapse cause both indicators increased. Secondly, with fast-slow variable dissection, the burst of bursting is identified to locate between a fold bifurcation and a big saddle-homoclinic orbit bifurcation of the fast subsystem. Enhanced excitatory or inhibitory autapses cannot induce changes of both bifurcation points, i.e., burst width. However, width of slow variable between two successive spikes within a burst becomes wider for the excitatory autapse and narrower for the inhibitory autapse, resulting in the less and more spikes per burst, respectively. Last, the autaptic current of fast autapse mainly plays a role during the peak of action potential, differing from the slow autaptic current with exponential decay, which can play roles following the peak of action potential. The fast excitatory autaptic current enhances the amplitude of the action potential and reduces the repolarization of the action potential to lengthen the interspike interval (ISI) of the spiking of the fast subsystem, resulting in the wide width of slow variable between successive spikes. The fast inhibitory autaptic current reduces the amplitude of action potential and ISI of spiking, resulting in narrow width of slow variable. The novel example of the paradoxical responses for both fast modulations and nonlinear mechanism extend the contents of neurodynamics, which presents potential functions of the fast autapse.
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Affiliation(s)
- Changsheng Qi
- College of Chemistry and Life Sciences, Chifeng University, Chifeng, 024000 China
| | - Yuye Li
- College of Mathematics and Computer Science, Chifeng University, Chifeng, 024000 China
| | - Huaguang Gu
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092 China
| | - Yongxia Yang
- College of Mathematics and Computer Science, Chifeng University, Chifeng, 024000 China
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Feali MS, Hamidi A. Dynamical response of Autaptic Izhikevich Neuron disturbed by Gaussian white noise. J Comput Neurosci 2023; 51:59-69. [PMID: 36040677 DOI: 10.1007/s10827-022-00832-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2022] [Revised: 06/16/2022] [Accepted: 08/14/2022] [Indexed: 01/18/2023]
Abstract
Using the improved memristive Izhikevich neuron model, the effects of autaptic connection as well as electromagnetic induction are studied on the dynamical behavior of neuronal spiking. Using bifurcation analysis for membrane potentials, the effects of autaptic and electromagnetic parameters on the mode transition in electrical activities of the neuron model are investigated. Furthermore, white Gaussian noise is considered in the neuron model, to evaluate the effect of electromagnetic disturbance on the firing pattern of the neuron using the coefficient of variation. The bifurcation diagram versus autaptic conductance and time delay has been extensively studied. The results show that the effects of autaptic connection as well as electromagnetic induction on the spiking behavior of neurons can be well demonstrated by using the Izhikevich model. The electrical activities of the Izhikevich neuron model become more complex when the effects of autaptic connection and electromagnetic induction are considered in the neuron model. Using the Izhikevich neuron model, the high variety of spiking/bursting patterns is represented in the bifurcation diagram of inter-spike interval versus autaptic or electromagnetic parameters. Noise can have distinct effects on the spiking activity of the neuron, for the subthreshold input current, increasing the intensity of the electromagnetic noise increases the regularity of the neuron spiking, but for the suprathreshold input current, the regularity of spiking decreases with noise.
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Affiliation(s)
- Mohammad Saeed Feali
- Department of Electrical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
| | - Abdolsamad Hamidi
- Electrical Engineering Department, Lorestan University, Khorramabad, Lorestan, Iran
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Bönsel F, Krauss P, Metzner C, Yamakou ME. Control of noise-induced coherent oscillations in three-neuron motifs. Cogn Neurodyn 2021; 16:941-960. [PMID: 35847543 PMCID: PMC9279551 DOI: 10.1007/s11571-021-09770-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2021] [Revised: 10/27/2021] [Accepted: 11/27/2021] [Indexed: 12/04/2022] Open
Abstract
The phenomenon of self-induced stochastic resonance (SISR) requires a nontrivial scaling limit between the deterministic and the stochastic timescales of an excitable system, leading to the emergence of coherent oscillations which are absent without noise. In this paper, we numerically investigate SISR and its control in single neurons and three-neuron motifs made up of the Morris–Lecar model. In single neurons, we compare the effects of electrical and chemical autapses on the degree of coherence of the oscillations due to SISR. In the motifs, we compare the effects of altering the synaptic time-delayed couplings and the topologies on the degree of SISR. Finally, we provide two enhancement strategies for a particularly poor degree of SISR in motifs with chemical synapses: (1) we show that a poor SISR can be significantly enhanced by attaching an electrical or an excitatory chemical autapse on one of the neurons, and (2) we show that by multiplexing the motif with a poor SISR to another motif (with a high SISR in isolation), the degree of SISR in the former motif can be significantly enhanced. We show that the efficiency of these enhancement strategies depends on the topology of the motifs and the nature of synaptic time-delayed couplings mediating the multiplexing connections.
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Affiliation(s)
- Florian Bönsel
- Chair for Dynamics, Control and Numerics, Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
- Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestr. 91, 91052 Erlangen, Germany
| | - Patrick Krauss
- Neuroscience Lab, University Hospital Erlangen, Friedrich-Alexander-Universität Erlangen-Nürnberg, Waldstr. 1, 91054 Erlangen, Germany
| | - Claus Metzner
- Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestr. 91, 91052 Erlangen, Germany
| | - Marius E. Yamakou
- Chair for Dynamics, Control and Numerics, Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
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Yang H, Xu G, Wang H. Effects of magnetic fields on stochastic resonance in Hodgkin-Huxley neuronal network driven by Gaussian noise and non-Gaussian noise. Cogn Neurodyn 2021; 16:707-717. [DOI: 10.1007/s11571-021-09734-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Revised: 09/13/2021] [Accepted: 10/13/2021] [Indexed: 01/01/2023] Open
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Liang X, Zhang X, Zhao L. Diversity-induced resonance for optimally suprathreshold signals. CHAOS (WOODBURY, N.Y.) 2020; 30:103101. [PMID: 33138465 DOI: 10.1063/5.0022065] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 09/17/2020] [Indexed: 05/25/2023]
Abstract
Recent research has revealed that a system of coupled units with a certain degree of parameter diversity can generate an enhanced response to a subthreshold signal compared to that without diversity, exhibiting a diversity-induced resonance. We here show that diversity-induced resonance can also respond to a suprathreshold signal in a system of globally coupled bistable oscillators or excitable neurons, when the signal amplitude is in an optimal range close to the threshold amplitude. We find that such diversity-induced resonance for optimally suprathreshold signals is sensitive to the signal period for the system of coupled excitable neurons, but not for the coupled bistable oscillators. Moreover, we show that the resonance phenomenon is robust to the system size. Furthermore, we find that intermediate degrees of parameter diversity and coupling strength jointly modulate either the waveform or the period of collective activity of the system, giving rise to the resonance for optimally suprathreshold signals. Finally, with low-dimensional reduced models, we explain the underlying mechanism of the observed resonance. Our results extend the scope of the diversity-induced resonance effect.
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Affiliation(s)
- Xiaoming Liang
- School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China
| | - Xiyun Zhang
- Department of Physics, Jinan University, Guangzhou, Guangdong 510632, China
| | - Liang Zhao
- Department of Computer Science and Mathematics, University of São Paulo, Ribeirão Preto 14040-901, Brazil
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