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Consider the competing species model x' = x(19-x-3y), a) Find the equilibrium at which both species coexist. x = 4, y = 5 Calculate the trace and determinant of the Jacobian matrix at this equilibrium: trace = 6, determinant = 6 The type of equilibrium is saddle ✔ The equilibrium is unstable b) Find the equilibrium at which population a survives and y is extinct. 19.y=0 Calculate the trace and determinant of the Jacobian matrix at this equilibrium: trace = -2, determinant = 5 The type of equilibrium is node The equilibrium is asymptotically stable y' = y(13 - 2x - y)

Consider the competing species model x' = x(19-x-3y), a) Find the equilibrium at which both species coexist. x = 4, y = 5 Calculate the trace and determinant of the Jacobian matrix at this equilibrium: trace = 6, determinant = 6 The type of equilibrium is saddle ✔ The equilibrium is unstable b) Find the equilibrium at which population a survives and y is extinct. 19.y=0 Calculate the trace and determinant of the Jacobian matrix at this equilibrium: trace = -2, determinant = 5 The type of equilibrium is node The equilibrium is asymptotically stable y' = y(13 - 2x - y)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the competing species model a) Find the equilibrium at which both species coexist. x = 4, y = 5 Calculate the trace and determinant of the Jacobian matrix at this equilibrium: trace = 6, determinant = 6 The type of equilibrium is saddle ✓ The equilibrium is unstable b) Find the equilibrium at which population survives and y is extinct. x=19.y=0 Calculate the trace and determinant of the Jacobian matrix at this equilibrium: trace = -2, determinant = 5 The type of equilibrium is node The equilibrium is asymptotically stable x = x(19x - 3y), V y = y(13 - 2x - y)
Transcribed Image Text:Consider the competing species model a) Find the equilibrium at which both species coexist. x = 4, y = 5 Calculate the trace and determinant of the Jacobian matrix at this equilibrium: trace = 6, determinant = 6 The type of equilibrium is saddle ✓ The equilibrium is unstable b) Find the equilibrium at which population survives and y is extinct. x=19.y=0 Calculate the trace and determinant of the Jacobian matrix at this equilibrium: trace = -2, determinant = 5 The type of equilibrium is node The equilibrium is asymptotically stable x = x(19x - 3y), V y = y(13 - 2x - y)
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