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The Fitzhugh-Nagumo model for the electric impulse in a neuron states that, in the absence of relaxation effects, the electric potential, v(t), in a neuron obeys the differential equation dvdt = −v(v2−(1+a)v+a) where a is a constant such that 0 < a < 1. Find and classify all equilibrium solutions and provide a phase line summarizing behavior of v(t). Hint: While the quadratic formula can be used, you can proceed more quickly by factoring!

The Fitzhugh-Nagumo model for the electric impulse in a neuron states that, in the absence of relaxation effects, the electric potential, v(t), in a neuron obeys the differential equation dvdt = −v(v2−(1+a)v+a) where a is a constant such that 0 < a < 1. Find and classify all equilibrium solutions and provide a phase line summarizing behavior of v(t). Hint: While the quadratic formula can be used, you can proceed more quickly by factoring!

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The Fitzhugh-Nagumo model for the electric impulse in a neuron states that, in the absence of relaxation effects, the electric potential, v ( t ) , in a neuron obeys the differential equation
d v d t = − v ( v 2 − ( 1 + a ) v + a )
where a is a constant such that 0 < a < 1 . Find and classify all equilibrium solutions and provide a phase line summarizing behavior of v ( t ) . Hint: While the quadratic formula can be used, you can proceed more quickly by factoring!

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