Question

The system

$x'=-y,y'=-\gamma y-x(x-0.15)(x-8)$

results from an approximation to the Hodgkin-Huxley equations, which model the transmission of neural impulses along an axon.

(a) Determine all critical points of the given system of equations. [Write your points in ascending order of their x-coordinates.]

$(x_{1},y_{1})=$ (___, ___)

$(x_{2},y_{2})=$ (___, ___)

(___, ___)

(b) Classify the critical points by investigating the approximate linear system near each one. **Choose one of the 3 in the () to fill in the blank**

The critical point $(x_{1},y_{1})$ is _______(a saddle, a node, a spiral) which is ______ (stable, unstable, asymptotically stable)

The critical point is _______(a saddle, a node, a spiral) which is ______ (stable, unstable, asymptotically stable)

The critical $(x_{3},y_{3})$ is _______(a saddle, a node, a spiral) which is ______ (stable, unstable, asymptotically stable)

(13-уз (x2, y2

Answer 1

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