Two-parameter bifurcation analysis of firing activities in the Chay neuronal model

Duan, Lixia; Lu, Qishao; Wang, Qinyun

doi:10.1016/j.neucom.2008.01.019

Cited by 68 publications

(32 citation statements)

References 25 publications

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“…14 a The two-parameter bifurcation diagram with respect to the slow variable C and the variable parameter V I ; b the enlargement of a part of a [114] Fig. 15 a "fold/fold" bursting; b "fold/Hopf" bursting; c "fold/homoclinic" bursting [114] the whole system was investigated in [114], based on the Izhikevich's classification scheme. Figure 14 shows the twoparameter bifurcation analysis of the fast subsystem with respect to the slow-varying parameter C and the control parameter V I [114].…”

Section: One-or Two-parameter Bifurcation Analysis For Neuronal Firinmentioning

confidence: 99%

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Yang

et al. 2008

Acta Mech Sin

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Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one-or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities (stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.).types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.

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Section: One-or Two-parameter Bifurcation Analysis For Neuronal Firinmentioning

confidence: 99%

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Yang

et al. 2008

Acta Mech Sin

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“…Bursting is ubiquitous in physical and biological systems, especially in neural systems where it plays an important role in information processing [34], and it is also thought to have significant functional roles in reliable signaling and synaptic plasticity [10]. Many models generating bursting have been subject to intensive research due to their physiological significance and dynamical complexity [14,16,28,[34][35][36]; the transition between different bursting patterns also attracted the interests of many researchers [12,17,[37][38][39]. Fast/slow bifurcation analysis is the most popular approach to study the bifurcation structure contained in the transition between different firing patterns.…”

Section: Discussionmentioning

confidence: 99%

“…For instance, Tsaneva-Atanasova et al [37,38] have used this approach to study the burst firing in endocrine cells. Duan et al conducted two-parameter analysis of firing activities in the Chay neuronal model using this approach [17]. Except for fast/slow analysis approach, the diagram of ISI is also a commonly used approach which can describe the transition among various firing patterns to some extent [16,[39][40][41].…”

Section: Discussionmentioning

confidence: 99%

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Burst firing transitions in two-compartment pyramidal neuron induced by the perturbation of membrane capacitance

et al. 2011

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Neuronal membrane capacitance C (m) is one of the prominent factors in action potential initiation and propagation and then influences the firing patterns of neurons. Exploring the roles that C (m) plays in different firing patterns can facilitate the understanding of how different factors might influence neuronal firing behaviors. However, the impacts of variations in C (m) on neuronal firing patterns have been only partly explored until now. In this study, the influence of C (m) on burst firing behaviors of a two-compartment pyramidal neuron (including somatic compartment and dendritic compartment) was investigated by means of computer simulation, the value of C (m) in each compartment was denoted as C (m,s) and C (m,d), respectively. Two cases were considered, in the first case, we let C (m,s) =C (m,d), and then changed them simultaneously. While in the second case, we assumed C (m,s) ≠C (m,d), and then changed them, respectively. From the simulation results obtained from these two cases, it was found that the variation of C (m) in the somatic compartment and the dendritic compartment show much difference, simulated results obtained from the variation of C (m,d) have much more similarities than that of C (m,s) when comparing with the results obtained in the first case under which C (m,s) =C (m,d). These different effects of C (m,s) and C (m,d) on neuronal firing behaviors may result from the different topology and functional roles of soma and dendrites. Numerical results demonstrated in this paper may give us some inspiration in understanding the possible roles of C (m) in burst firing patterns, especially their transitions in compartmental neurons.

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“…Shilnikov [27] had summarized the qualitative methods on HindmarshRose model, and presented the different burstings under Hopf bifurcation. Lu [28] proposed a double-parameter analysis method to reveal the complex behaviors of Chay models. Bi [29,30] investigated the periodic excited systems and non-smooth systems, and discussed the connection of bursting with bifurcations such as Fold, Hopf, and non-smooth bifurcations.…”

Section: Introductionmentioning

confidence: 99%

Slow-fast effect and generation mechanism of brusselator based on coordinate transformation

Hou

Shen

2016

Open Physics

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Abstract:The Brusselator with different time scales, which behaves in the classical slow-fast effect, is investigated, and is characterized by the coupling of the quiescent and spiking states. In order to reveal the generation mechanism by using the slow-fast analysis method, the coordinate transformation is introduced into the classical Brusselator, so that the transformed system can be divided into the fast and slow subsystems. Furthermore, the stability condition and bifurcation phenomenon of the fast subsystem are analyzed, and the attraction domains of different equilibria are presented by theoretical analysis and numerical simulation respectively. Based on the transformed system, it could be found that the generation mechanism between the quiescent and spiking states is Fold bifurcation and change of the attraction domain of the fast subsystem. The results may also be helpful to the similar system with multiple time scales.

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Two-parameter bifurcation analysis of firing activities in the Chay neuronal model

Cited by 68 publications

References 25 publications

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

Burst firing transitions in two-compartment pyramidal neuron induced by the perturbation of membrane capacitance

Slow-fast effect and generation mechanism of brusselator based on coordinate transformation

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