Bursting mechanism in a time-delayed oscillator with slowly varying external forcing

Yu, Yue; Tang, Hongji; Han, Xiujing; Bi, Qinsheng

doi:10.1016/j.cnsns.2013.08.010

Cited by 21 publications

(10 citation statements)

References 27 publications

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“…ApEn algorithm has some anti-noise ability itself, and thus effect of different filtering methods can be reduced [19,31]. The amount of data is not so demanding (500-4000 points is generally enough) and some fast computation of ApEn has been developed, which makes the execution time shorter than other nonlinear algorithm [32,33].…”

Section: The Apen Extraction Algorithmmentioning

confidence: 99%

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Analysis of Neural Oscillations on Drosophila’s Subesophageal Ganglion Based on Approximate Entropy

Tian

Qiao

Zhou

et al. 2015

Entropy

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Abstract:The suboesophageal ganglion (SOG), which connects to both central and peripheral nerves, is the primary taste-processing center in the Drosophila's brain. The neural oscillation in this center may be of great research value yet it is rarely reported. This work aims to determine the amount of unique information contained within oscillations of the SOG and describe the variability of these patterns. The approximate entropy (ApEn) values of the spontaneous membrane potential (sMP) of SOG neurons were calculated in this paper. The arithmetic mean (MA), standard deviation (SDA) and the coefficient of variation (CVA) of ApEn were proposed as the three statistical indicators to describe the irregularity and complexity of oscillations. The hierarchical clustering method was used to classify them. As a result, the oscillations in SOG were divided into five categories, including: (1) Continuous spike pattern; (2) Mixed Steady oscillation state has a low level of irregularity, and vice versa. The dopamine stimulation can distinctly cut down the complexity of the mixed oscillation pattern. The current study provides a quantitative method and some critera on mining the information carried in neural oscillations.

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Section: The Apen Extraction Algorithmmentioning

confidence: 99%

“…By comparison various setting [31], we set m = 2 and r = 0.25 SD(u) here (SD is the standard deviation). In the present study, 2000 sampling points were computed once, equal to ApEn of one second.…”

Section: The Apen Extraction Algorithmmentioning

confidence: 99%

Analysis of Neural Oscillations on Drosophila’s Subesophageal Ganglion Based on Approximate Entropy

Tian

Qiao

Zhou

et al. 2015

Entropy

View full text Add to dashboard Cite

show abstract

“…It has also been shown that time delays may have a significant impact on bursting behaviors. For example, time delays can suppress bursting, lead to more complex dynamic [Zheng & Wang, 2012], and change both qualitative and quantitative properties of bursting patterns [Han & Bi, 2011;Yu et al, 2014].…”

Section: Introductionmentioning

confidence: 99%

Delayed Bifurcations to Repetitive Spiking and Classification of Delay-Induced Bursting

Han

Zhang

et al. 2014

Int. J. Bifurcation Chaos

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Three new routes to repetitive spiking, i.e. the delayed transcritical bifurcation, the delayed supercritical pitchfork bifurcation and the delayed subcritical pitchfork bifurcation, are revealed in this paper. We use bifurcation theory to classify bursting patterns related to three such delayed bifurcations. Then many new bursting patterns are obtained, including 24 new bursting patterns of point-point type, 27 new bursting patterns of point-cycle type and three new bursting patterns of point-torus type. Our study suggests that the classification of bursting remains to be further explored, since many new bursting patterns may be obtained based on new routes to repetitive spiking, even though we just consider codimension-1 bifurcations.

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“…The studies of bursting or mixed-mode oscillations have received great attention recently in modeling realistic neuronal networks, physics, chemistry, mechanics and engineering systems and so on [1][2][3]. Bursting oscillations are waveforms that consist of alternating small and large amplitude excursions.…”

Section: Introductionmentioning

confidence: 99%

Modified function projective bursting synchronization for fast–slow systems with uncertainties and external disturbances

Gao

Han

et al. 2014

Nonlinear Dyn

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This paper addresses the modified function projective bursting synchronization (MFPBS) for a class of fast-slow systems with uncertainties and external disturbances. By using an active sliding mode control method (SMC), bursting synchronization can occur between two different chaotic systems. An active SMC law is established to guarantee uncertainties and disturbances rejection and realize the MFPBS. The sufficient condition is drawn for the stability of error dynamics, where the controllers are designed by using the relevant variables in fast-slow systems. More interestingly, more complex bursting oscillations such as chaotic bursting, as well as chaotic or periodic spiking can be obtained in slave systems with free scales when the MFPBS is maintained. And the corresponding numerical simulation is provided to illustrate the effectiveness of the proposed method.

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Bursting mechanism in a time-delayed oscillator with slowly varying external forcing

Cited by 21 publications

References 27 publications

Analysis of Neural Oscillations on Drosophila’s Subesophageal Ganglion Based on Approximate Entropy

Analysis of Neural Oscillations on Drosophila’s Subesophageal Ganglion Based on Approximate Entropy

Delayed Bifurcations to Repetitive Spiking and Classification of Delay-Induced Bursting

Modified function projective bursting synchronization for fast–slow systems with uncertainties and external disturbances

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