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

Abstract

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.

Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns

“…A method to detect unstable periodic orbits (UPOs), based on an algorithm of enhancing density (So et al 1996(So et al , 1997(So et al , 1998 and tested in a series of studies Gu et al 2004Gu et al , 2007Lu et al 2008;Yang et al 2009), is employed in this paper.…”

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

“…So far, many investigations have been made for analyzing dynamics of bursting oscillations, and some important methods were proposed to uncover the bifurcation mechanism of transition between QS and SS. Two important bifurcations can be found associated with the busters: bifurcation of a quiescent state which leads to repetitive spiking and bifurcation of a spiking attractor that leads to quiescence [10][11][12].…”

Bursting oscillations in Duffing’s equation with slowly changing external forcing

“…Bursting oscillations are waveforms that consist of alternating small and large amplitude excursions. Such oscillations have been reported in both experiments and models of systems from chemistry [1][2][3], biochemistry [4][5][6], physics [7,8] and neuroscience [9][10][11][12][13][14]. In fact, bursting oscillations are often observed to occur in signal transduction processes and are associated with many biological phenomena, such as oscillatory enzyme responses [4], insulin production in the b-cell [10] and veratridine in rat injured sciatic nerves [11].…”