Equilibrium Points: The model has equilibrium points where both populations remain constant over time. These equilibrium points can be stable or unstable, depending on the values of the model parameters. A stable equilibrium represents a situation where predator and prey popula- tions coexist in a relatively stable manner. In the Lotka-Volterra Model it is rare to find perfect equilibrium solutions, more often the solutions exhibit oscillatory behaviour around the equilibrium points rather than staying at them. To find the equilibrium points for this system we set both dx/dt and dy/dt to zero and solve dx = ax - bxy dt dy dt == -cy + dxy We find we have 2 sets of equilibrium values, (0,0) when both predator and prey populations vanish, and (c/d, a/b) when there are just enough prey to support a constant predator population but there are not too many predators. Answer the following question for the system shown below. dx dt = 2.4x-1.2xy 33 dy dt = −y + xy 11. Find the equilibrium values for the system and use the Slopes App Phase Plane Activityto graph a solution in the plase plane with intial conditions as close as you can get to the equilibrium value. Upload your file to GS showing both the solution and the phase plane portrait.

Equilibrium Points: The model has equilibrium points where both populations remain constant over time. These equilibrium points can be stable or unstable, depending on the values of the model parameters. A stable equilibrium represents a situation where predator and prey popula- tions coexist in a relatively stable manner. In the Lotka-Volterra Model it is rare to find perfect equilibrium solutions, more often the solutions exhibit oscillatory behaviour around the equilibrium points rather than staying at them. To find the equilibrium points for this system we set both dx/dt and dy/dt to zero and solve dx = ax - bxy dt dy dt == -cy + dxy We find we have 2 sets of equilibrium values, (0,0) when both predator and prey populations vanish, and (c/d, a/b) when there are just enough prey to support a constant predator population but there are not too many predators. Answer the following question for the system shown below. dx dt = 2.4x-1.2xy 33 dy dt = −y + xy 11. Find the equilibrium values for the system and use the Slopes App Phase Plane Activityto graph a solution in the plase plane with intial conditions as close as you can get to the equilibrium value. Upload your file to GS showing both the solution and the phase plane portrait.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...

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