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7. Consider the system: dx | | = -2x+4xy dt 2y y (1 --1/2) - - 3xy dy dt (a) Are these species predator-prey or competing? = (b) What type of growth/decay does species x exhibit in absence of species y? What type of growth/decay does species y exhibit in absence of species x? (c) Find all critical (equilibrium) points. (d) 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.

7. Consider the system: dx | | = -2x+4xy dt 2y y (1 --1/2) - - 3xy dy dt (a) Are these species predator-prey or competing? = (b) What type of growth/decay does species x exhibit in absence of species y? What type of growth/decay does species y exhibit in absence of species x? (c) Find all critical (equilibrium) points. (d) 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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 19RE
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7. Consider the system: dx | | = -2x+4xy dt 2y y (1 --1/2) - - 3xy dy dt (a) Are these species predator-prey or competing? = (b) What type of growth/decay does species x exhibit in absence of species y? What type of growth/decay does species y exhibit in absence of species x? (c) Find all critical (equilibrium) points. (d) 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.
Transcribed Image Text:7. Consider the system: dx | | = -2x+4xy dt 2y y (1 --1/2) - - 3xy dy dt (a) Are these species predator-prey or competing? = (b) What type of growth/decay does species x exhibit in absence of species y? What type of growth/decay does species y exhibit in absence of species x? (c) Find all critical (equilibrium) points. (d) 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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