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Consider a nonlinear system for two populations with equilibrium points (0, 0), (0, N), (.), and Jacobian * J(z,y) = [1 2x+y -V -z+N-2y. ↓ 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>N (0,0) is a (O.N) is a (4.4) c) Sketch the geometric behavior of these solutions in the first quadrant of the phase plane (y vs x) for N-2

Consider a nonlinear system for two populations with equilibrium points (0, 0), (0, N), (.), and Jacobian * J(z,y) = [1 2x+y -V -z+N-2y. ↓ 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>N (0,0) is a (O.N) is a (4.4) c) Sketch the geometric behavior of these solutions in the first quadrant of the phase plane (y vs x) for N-2

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 a nonlinear system for two populations with equilibrium points (0, 0), (0, N), (4,4), and Jacobian x -[-² -2x+y -y -z+N-2y J(x, y) = 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>N: (0,0) is a (O.N) is a c) Sketch the geometric behavior of these solutions in the first quadrant of the phase plane (y vs x) for N-2
Transcribed Image Text:Consider a nonlinear system for two populations with equilibrium points (0, 0), (0, N), (4,4), and Jacobian x -[-² -2x+y -y -z+N-2y J(x, y) = 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>N: (0,0) is a (O.N) 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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