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Publication Type : Journal Article
Publisher : International Journal of Pure and Applied Mathematics
Source : International Journal of Pure and Applied Mathematics, Volume 118, Number 20, p.3979-3985 (2018)
Keywords : action potential, Chaos, excitation, Hodgkin-Huxley, Hopf bifurcation, Inhibition, Membrane Potential, Neuronal Synchronization, Synaptic coupling, Synchronization
Campus : Bengaluru
School : School of Engineering
Department : Electronics and Communication
Year : 2018
Abstract : The flow of information from various parts of the body to the brain and vice versa is facilitated through neurons. The nervous system consists of large number of such neurons interconnected together. Computational neuroscience is the branch of study , which deals with the information processing capabilities of the structures that form the nervous system. This study motivates us to come up with a mathematical model where we can simulate and test the information processing functionality of various parts of the nervous system and also to help in developing therapeutical solutions for various pathological disorders . In this paper , an attempt has been made to illustrate and simulate the information transfer via neurons using a simple mathematical simulation model consisting of Hodgkin-Huxley (HH) neurons . Starting with a group of two and four neurons we have simulated the information transfer from one neuron to the another and then further extended it to create oscillations or the chaotic activity . The chaotic activity among the network of neurons at the microscopic level helps to control the flow of information at the macroscopic level . At the microscopic level the information is propagated from one neuron to the other in the form of action potentials whereas at the macroscopic level the flow of information happens in the form of oscillations. In order to achieve this state appropriate selection of coupling coefficients for both excitatory and inhibitory connections is important . The selection of coupling coefficient has to be in such a way that there should be a trade of between firing and Hopf Bifurcation. We also aim to simulate and illustrate the mechanism of synaptic plasticity and how it impacts the firing of post synaptic neurons . These oscillations selectively respond to small fluctuations and are capable of rapid state transitions . This enables the sensory inputs at microscopic level to control the macroscopic activity that constitutes the cortical output.
Cite this Research Publication : S. Nair, R. Sunitha, Pradhan, N., and Sreedevi, A., “Modelling and simulation of neuronal communications at microscopic and macroscopic level”, International Journal of Pure and Applied Mathematics, vol. 118, pp. 3979-3985, 2018.