.The system x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7)x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7) is a special case of the Fitzhugh–Nagumo16 equations, which model the transmission of neural impulses along an axon. The parameter k is the external stimulus. a.Show that the system has one critical point regardless of the value of k.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
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.The system

x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7)x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7)

is a special case of the Fitzhugh–Nagumo16 equations, which model the transmission of neural impulses along an axon. The parameter k is the external stimulus.

a.Show that the system has one critical point regardless of the value of k.

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