Variability of bursting patterns in a neuron model in the presence of noise |
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Authors: | Paul Channell Ibiyinka Fuwape Alexander B Neiman Andrey L Shilnikov |
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Institution: | (1) Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA;(2) Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA;(3) Department of Physics, Federal University, of Technology, Akure, PMB 704, Nigeria;(4) The Neuroscience Institute, Georgia State University, Atlanta, GA 30303, USA;; |
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Abstract: | Spiking and bursting patterns of neurons are characterized by a high degree of variability. A single neuron can demonstrate
endogenously various bursting patterns, changing in response to external disturbances due to synapses, or to intrinsic factors
such as channel noise. We argue that in a model of the leech heart interneuron existing variations of bursting patterns are
significantly enhanced by a small noise. In the absence of noise this model shows periodic bursting with fixed numbers of
interspikes for most parameter values. As the parameter of activation kinetics of a slow potassium current is shifted to more
hyperpolarized values of the membrane potential, the model undergoes a sequence of incremental spike adding transitions accumulating
towards a periodic tonic spiking activity. Within a narrow parameter window around every spike adding transition, spike alteration
of bursting is deterministically chaotic due to homoclinic bifurcations of a saddle periodic orbit. We have found that near
these transitions the interneuron model becomes extremely sensitive to small random perturbations that cause a wide expansion
and overlapping of the chaotic windows. The chaotic behavior is characterized by positive values of the largest Lyapunov exponent,
and of the Shannon entropy of probability distribution of spike numbers per burst. The windows of chaotic dynamics resemble
the Arnold tongues being plotted in the parameter plane, where the noise intensity serves as a second control parameter. We
determine the critical noise intensities above which the interneuron model generates only irregular bursting within the overlapped
windows. |
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