International Journal of Engineering Technology Science and Research
IJETSR
www.ijetsr.com
ISSN 2394 – 3386
Volume 3, Issue 9
September 2016
Hopfield Model of a Neuron Dynamics under External
Stimulus
Dr. Vandana Gupta1 , Dr. S.K.Tiwari2, Raghvendra Singh3
1Professor & Head, Department of Mathematics, Govt. Kalidas Girls College, Ujjain(M.P.)
2Reader ,School of Studies in Mathematics, Vikram University, Ujjain(M.P.)
3 School of Studies in Mathematics, Vikram University, Ujjain(M.P.)
Abstract:
In this paper, we have presented Hopfield Model of a Neuron Dynamics under external stimulus. In this model we have
taken a nonlinear integro-differential equation in the presence of external stimulus without any self -feedback. We have
shown that the solution is bounded and not closed curve in Phase plane. Some conditions ensure the existence and
uniqueness of equilibrium point that are derived.
Keywords: Equilibrium point, Lyapunov functional, Boundary conditions, Bendixson’s criteria.
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Dr. Vandana Gupta , Dr. S.K.Tiwari, Raghvendra Singh