ASSIGNMENT 2.6
This assignment is to be submitted to the assignment box by noon on Friday, March 18. It does not have to
be typeset, though it must be legible and well-written.
Include your full name and student ID, along with the subject and assignment number, at the top of the front
page.
1. Sketch the phase plane, including a few representative trajectories, for the system of equations
dx
dt
dy
dt
= y − x2
.
= x−1
2. Write down a system of differential equations describing the populations of lions and hyenas in the African
savannah. Justify the equations and describe their shortcomings.
3. The following system of differential equations, called a FitzHugh-Nagumo model, describes the interaction between the membrane potential and action potential of a spiking neuron. Here, v represents the
membrane potential and w represents the sodium gating variable:
dv
dt
dw
dt
=
f (v + 0.07) − f (0.07) − w
=
0.008(v − 2.54w)
, where f (v) = v(v − 0.139)(1 − v).
Sketch the phase plane, including a few representative trajectories. (Hint: not all the nullclines are linear.)