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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E

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Question

Consider a nonlinear system for two populations with equilibrium points (0, 0), (0, N), (,), and Jacobian
x
J(2,3) = [
-2x+y
-Y
-x+N-2y
b
a) What is the critical bifurcation value. Ne, which changes the number of eq. pts.?
b) Evaluate the Jacobian at each equilibrium point and determine eq, pt. type for N>N₂:
(0,0) is a
(O.N) is a
() is a
c) Sketch the geometric behavior of these solutions in the first quadrant of the phase plane (y vs x) for N-2.

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