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California State Polytechnic University, Pomona

# The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electrical potential in a neuron $v(t)$ obeys the differential equation $\frac {dv}{dt} = - v [v^2 - (1 + a) v + a]$ where $a$ is a positive constant such that $0 < a < 1.$(a) For what values of $v$ is $v$ unchanging (that is, $dv/dt = 0)?.$(b) For what values of $v$ is $v$ increasing?(c) For what values of $v$ is $v$ decreasing?

## (a) $\frac{d v}{d t}=0$ when $v=0,1, a$(b) $v$ is increasing when $v \in(-\infty, 0) \cup(a, 1)$(c) $v$ is decreasing when $v \in(0, a) \cup(1, \infty)$

#### Topics

Differential Equations

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MS

Matt S.

October 22, 2021

Thank you for the detailed solution

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