dx/dt=4x(1-2x)-xy dy/dt=2y-4xy (a) Find all critical (equilibrium) points. (b) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point.

dx/dt=4x(1-2x)-xy dy/dt=2y-4xy (a) Find all critical (equilibrium) points. (b) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 31E

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Question

Consider the system:

dx/dt=4x(1-2x)-xy

dy/dt=2y-4xy

(a) Find all critical (equilibrium) points.

(b) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point.

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