In a pond, green sunfish competes with bluegill for food. Let z, y be the amount of green sunfish and bluegill respectively (in thousands). Suppose that the interaction of the green sunfish and the bluegill is described by the system a' = 3x – a? – ry, (1) (2) y = 3y – 2y? – 0.5xy • Find all critical points of this system. • Compute Jacobian matrices of the system at the critical points; determine types of these points if possible (saddle, nodal source/sink, spiral source/sink). Sketch the phase portrait of the (nonlinear) system in the domain a > 0, y > 0 (cv. examples 3,4 in Sec. 6.3). • Make a conclusion: can green sunfish and bluegill peacefully coexist in the pond? If yes, use the picture to find limit sizes of populations lim 100 #(t), lim, +00 Y(t).

In a pond, green sunfish competes with bluegill for food. Let z, y be the amount of green sunfish and bluegill respectively (in thousands). Suppose that the interaction of the green sunfish and the bluegill is described by the system a' = 3x – a? – ry, (1) (2) y = 3y – 2y? – 0.5xy • Find all critical points of this system. • Compute Jacobian matrices of the system at the critical points; determine types of these points if possible (saddle, nodal source/sink, spiral source/sink). Sketch the phase portrait of the (nonlinear) system in the domain a > 0, y > 0 (cv. examples 3,4 in Sec. 6.3). • Make a conclusion: can green sunfish and bluegill peacefully coexist in the pond? If yes, use the picture to find limit sizes of populations lim 100 #(t), lim, +00 Y(t).

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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