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      NEURAL EXCITABILITY, SPIKING AND BURSTING

      1 , 2
      International Journal of Bifurcation and Chaos
      World Scientific Pub Co Pte Lt

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          Abstract

          Bifurcation mechanisms involved in the generation of action potentials (spikes) by neurons are reviewed here. We show how the type of bifurcation determines the neuro-computational properties of the cells. For example, when the rest state is near a saddle-node bifurcation, the cell can fire all-or-none spikes with an arbitrary low frequency, it has a well-defined threshold manifold, and it acts as an integrator; i.e. the higher the frequency of incoming pulses, the sooner it fires. In contrast, when the rest state is near an Andronov–Hopf bifurcation, the cell fires in a certain frequency range, its spikes are not all-or-none, it does not have a well-defined threshold manifold, it can fire in response to an inhibitory pulse, and it acts as a resonator; i.e. it responds preferentially to a certain (resonant) frequency of the input. Increasing the input frequency may actually delay or terminate its firing.

          We also describe the phenomenon of neural bursting, and we use geometric bifurcation theory to extend the existing classification of bursters, including many new types. We discuss how the type of burster defines its neuro-computational properties, and we show that different bursters can interact, synchronize and process information differently.

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          Most cited references74

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          A quantitative description of membrane current and its application to conduction and excitation in nerve

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            Voltage oscillations in the barnacle giant muscle fiber.

            Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.
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              Excitatory and inhibitory interactions in localized populations of model neurons.

              Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency of the limit cycle oscillation is found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics in response to one class of stimuli implies the existence of multiple stable states and hysteresis in response to a different class of stimuli. The relation between these findings and a number of experiments is discussed.
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                Author and article information

                Journal
                International Journal of Bifurcation and Chaos
                Int. J. Bifurcation Chaos
                World Scientific Pub Co Pte Lt
                0218-1274
                1793-6551
                May 02 2012
                June 2000
                May 02 2012
                June 2000
                : 10
                : 06
                : 1171-1266
                Affiliations
                [1 ]The Neurosciences Institute, 10640 John Jay Hopkins Drive, San Diego, CA 92121, USA
                [2 ]Center for Systems Science & Engineering, Arizona State University, Tempe, AZ 85287-7606, USA
                Article
                10.1142/S0218127400000840
                21340263-21bd-4698-af22-bcb306e0545c
                © 2000
                History

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