What is it about?
The distinct qualitative behavior exhibited by neuron at externally applied current stimuli is well known in the Hodgkin Huxley model (HH model). The resting state and periodic firings in neurons correspond to solutions of the HH model having stable fixed points and unstable fixed points (periodic solutions through Hopf bifurcation points). The one-parameter bifurcation with respect to externally applied current stimuli suggests a periodic window between two stable fixed point solutions in the HH model. The externally applied sinusoidal current stimuli generate periodic firings at very low current and a large periodic region is observed. The generations of limit cycles and possible chaotic behavior in the HH model is explored through numerical simulations extensively.
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Why is it important?
The network of neurons in the brain is very complex and study about its dynamics is also very complicated. We have tried to analyze the effect of externally applied current on neuron response. The different behavior of externally applied current shows the dynamics of the neurons. This study helps to understand the behavior of neurons.
Perspectives
Brain is very important and interesting part of body. I am very much interested in dynamics of brain. Communication of neurons via electrical signals are the key factor for the function of human body. Patterns of neuron firings are amazing to observe. This study helps people who do not belong to the neuroscience subject to understand the dynamics of the brain.
Dr. Avinita Gautam
CNR, Rome, Italy
Read the Original
This page is a summary of: Periodic firings in neurons with external sinusoidal applied current, Journal of Mathematical and Computational Science, January 2019, SCIK Publishing Corporation,
DOI: 10.28919/jmcs/4223.
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