Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models

Белых, В. Н.; Belykh, Igor; Colding‐Jørgensen, Morten; Mosekilde, Erik

doi:10.1007/s101890070012

Cited by 69 publications

(76 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The combination of modeling and experimental results show that the transitions between various patterns of firing activities are consistent with the idea that the system moves through period doubling bifurcations [96]. Belykh [97] presented a qualitative analysis of a generic model structure that could simulate bursting and spiking dynamics of many biological cells, and four different scenarios for the emergence of bursting were described.…”

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

confidence: 52%

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

Yang

et al. 2008

Acta Mech Sin

View full text Add to dashboard Cite

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.

show abstract

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

confidence: 52%

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

Yang

et al. 2008

Acta Mech Sin

View full text Add to dashboard Cite

show abstract

“…To understand this double behavior, the system must be analyzed as the interaction between a 2D fast subsystem and the influence of a slow variable working as a parameter. As discussed by Belykh et al [48], this approach is incomplete and, for instance, cannot explain the existence of chaotic dynamics. However, it is sufficient for our purposes.…”

Section: A Evolution Of Nsb In the Presence Of Noisementioning

confidence: 99%

Analysis of the noise-induced bursting-spiking transition in a pancreaticβ-cell model

2004

View full text Add to dashboard Cite

A stochastic model of the electrophysiological behavior of the pancreatic ␤ cell is studied, as a paradigmatic example of a bursting biological cell embedded in a noisy environment. The analysis is focused on the distortion that a growing noise causes to the basic properties of the membrane potential signals, such as their periodic or chaotic nature, and their bursting or spiking behavior. We present effective computational tools to obtain as much information as possible from these signals, and we suggest that the methods could be applied to real time series. Finally, a universal dependence of the main characteristics of the membrane potential on the size of the considered cell cluster is presented.

show abstract

“…It is known that constructing a low-dimensional system of differential equation which is capable of generating fast spikes bursts excited on top of the slow oscillations, one needs to consider a system which has both slow and fast dynamics (see for example [7][8][9][10][11]). Using the same approach one can construct a two-dimensional map, which can be written in the form…”

Section: Introductionmentioning

confidence: 99%

Modeling of spiking-bursting neural behavior using two-dimensional map

2002

View full text Add to dashboard Cite

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps which model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activity of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons. PACS number(s): 05.45.+b, 87.22.-q

show abstract

Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models

Cited by 69 publications

References 22 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

Analysis of the noise-induced bursting-spiking transition in a pancreaticβ-cell model

Modeling of spiking-bursting neural behavior using two-dimensional map

Contact Info

Product

Resources

About